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Arithmetic and Geometric Sequences Recursive and Explicit Formulas Day 2 Notation: t1 = first term in the sequence tn = the n th term tn-1 = the term BEFORE the n th term d = common difference (could be negative) r = common ratio (could be fraction)

Arithmetic and Geometric Sequences Recursive and Explicit ...

Arithmetic and Geometric Sequences Recursive and Explicit Formulas Day 2 Notation: t1 = first term in the sequence tn = the n th term tn-1 = the term BEFORE the n th term d = common difference (could be negative) r = common ratio (could be fraction)

6-3 Geometric Sequences in Recursive Form

6-3 Geometric Sequences in Recursive Form 256 Lesson 6-3 Geometric Sequences in Recursive Form. Problem 2 Problem 1 Writing a Recursive Formula for a Geometric Sequence Find the recursive formula for the sequence 7, 21, 63, 189, . . . . The starting value A (1) is 7. The common ratio r is 21

8.3 ARITHMETIC AND GEOMETRIC SEQUENCES

and the sequences are generated by regularly adding the same number (thecom-mon difference in an arithmetic sequence) or multiplying by the same number (the common ratio in a geometric sequence). Deﬁnitions emphasize the parallel fea-tures, which examples will clarify. Deﬁnition: arithmetic and geometric sequences Arithmetic Sequence a 1 5 ...

Arithmetic and Geometric Sequences - VDOE

Arithmetic and Geometric Sequences Reporting Category Number and Number Sense Topic Describing arithmetic and geometric sequences . Primary SOL . 7.2 The student will describe and represent arithmetic and geometric sequences, using variable expressions. Related SOL . 7.13a write verbal expressions as algebraic expressions and sentences as

Concept 16: Arithmetic & Geometric Sequences

Concept 16 Arithmetic & Geometric Sequences Concept 16: Arithmetic & Geometric Sequences Assessment (Level 4 Example Question Level 3 Example Question Level 2 Example Question Write an equation for this geometric sequence and find the 10th term of the sequence. 3, 6, 12, 24, 48, … Write an equation for this arithmetic sequence and find the

Arithmetic and geometric sequences SAMPLE

What is a geometric sequence? How do we find the nth term of an arithmetic or geometric sequence? How do we find the sum of the first nterms of an arithmetic or geometric sequence? How do we find the sum to infinity of a geometric sequence? How can we use arithmetic and geometric sequences to model real-world situations?

Arithmetic and Geometric Sequences Worksheet

Arithmetic and Geometric Sequences Worksheet Arithmetic Sequence - is a sequence of terms that have a common _____ between them. General Term: Geometric Sequence - is a sequence of terms that have a common _____ between them. General Term: 1. Are the following sequences arithmetic, geometric, or neither? If they are arithmetic, state the value ...

Lesson 3: Arithmetic and Geometric Sequences - EngageNY

Lesson 3: Arithmetic and Geometric Sequences Student Outcomes Students learn the structure of arithmetic and geometric sequences. Lesson Notes In this lesson, students will use their knowledge of sequences developed in Lessons 1 and 2 to differentiate between arithmetic and geometric sequences.

Arithmetic and Geometric Sequences and Series ... - RPDP

Arithmetic and Geometric Sequences and Series Reporting Category Expressions and Operations Topic Exploring sequences and series Primary SOL AII.2 The student will investigate and apply the properties of arithmetic and geometric sequences and series to solve real-world problems, including writing the first n terms, finding the nth term, and

Secondary I - 4.3 Arithmetic and Geometric Sequences Worksheet

4.3 Arithmetic and Geometric Sequences Worksheet Determine if the sequence is arithmetic. If it is, find the common difference. ... Given the first term and the common difference of an arithmetic sequence find the explicit formula and the three terms in the sequence after the last one given. 45) a 1 = 35 , d = −20 46) a 1

Assignment: Rules for Arithmetic and Geometric Sequences

Part I: Use Rules to Determine Sequences 1. Use the rule tn n 3 55 to find the first five terms in the arithmetic sequence. 2. Use the rule 52n 1 t n to find the first five terms in the geometric sequence. Part II: Write Rules for Arithmetic and Geometric Sequences 3. Identify the common difference OR common ratio, depending on whether the sequence

Arithmetic and Geometric Sequences and Series ... - VDOE

Create a real-life situation in which a geometric series would be used. Compare the use of the . rules for arithmetic series and arithmetic sequences with summation notation (∑) for an arithmetic series. Explain w. hat the common ratio . cannot. be if we are to calculate an infinite series, and

ARITHMETIC AND GEOMETRIC SEQUENCES COMMON CORE ALGEBRA ...

The first term of an arithmetic sequence whose common difference is 7 and whose 22nd term is given by a22 143 is which of the following? (1) 25 (3) 7 (2) 4 (4) 28 Answer Key 21 32 43 4242 4246 46410 aa aa ... CCAlgII.Unit-5.Lesson-2.Arithmetic-and-Geometric-Sequences.Answer-Key Author: Cecilia Doody

Recursive and Explicit definitions Recursive definition - Quia

Recursive and Explicit definitions : Recursive definition ... The explicit definition allows you to calculate any term in a sequence by using the first term and the common difference (ratio) between terms. ... Relations and Functions : Relation A relation is a set of any ordered pairs (x,y).

Explicit Expressions and Recursive Processes Independent ...

Explicit Expressions and Recursive Processes - Independent Practice Worksheet Complete all the problems. 1. Write a recursive formula for the following sequences. 2, 5, 26, 677… 2. Given the recursive formula, write the explicit formula for the sequence. t1 = 0, tn = tn-1 - 2 3. Write an explicit formula for the following sequences.

Recursive Sequences - Mathematics

Recursive Sequences We have described a sequence in at least two different ways: a list of real numbers where there is a ﬁrst number, a second number, and so on. ... A recursive formula always has two parts: 1.the starting value for the ﬁrst term a0; 2.the recursion equation for an as a function of an1 (the term before it.)

Lesson 2: Recursive Formulas for Sequences - EngageNY

Lesson 2: Recursive Formulas for Sequences Student Outcomes Students write recursive and explicit formulas for sequences. Lesson Notes In this lesson, students will work on recursive formulas building on the ideas that were introduced in Module 1, Lessons 26 and 27 (The Double and Add 5 Game). Classwork Opening (2 minutes)

Exploring Arithmetic Sequences using the TI-84 Plus

Exploring Arithmetic Sequences using the TI-84 Plus Troy Hayes Utica Community Schools Email: [email protected] Lesson Snapshot: This is an introductory lesson to arithmetic sequences. Students will begin by exploring a tessellation of an equilateral triangle using Cabri Jr. The general form of an arithmetic sequence

Arithmetic Sequences - projectmaths.ie

Less able students may engage with the activities in a relatively straightforward way while the more able students should engage in more open-ended and challenging activities. In this Teaching and Learning Plan, for example teachers can provide students with different applications of arithmetic sequences and with appropriate amounts and

I Arithmetic Sequences 1) 2) Determine whether each ...

MPS21/MRS22- LESSON-13 Mr. Pineda Aim: What is an Arithmetic Sequence? (Section 9-2) 1 | P a g e Student Version Do Now: I – Arithmetic Sequences 1) 2) Determine whether each sequence is arithmetic.

12.3 ARITHMETIC SEQUENCES AND SERIES

ARITHMETIC SEQUENCES AND SERIES ... Write a formula for the nth term of the arithmetic sequence 5, 9, 13, 17, 21, . . . . Solution ... The nth term of an arithmetic sequence with ﬁrst term a1 and common difference d is given by the formula an a1 nd. False 5.

13.3 ARITHMETIC SEQUENCES AND SERIES

Arithmetic Series The indicated sum of an arithmetic sequence is called an arithmetic series.For example, the series 2 4 6 8 10 54 is an arithmetic series because there is a common difference of 2 between the terms. We can ﬁnd the actual sum of this arithmetic series without adding all of the terms.

Arithmetic Sequences and Sums - Math is Fun

Arithmetic Sequences and Sums Sequence. A Sequence is a set of things (usually numbers) that are in order.. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details.. Arithmetic Sequence. In an Arithmetic Sequence the difference between one term and the next is a constant.. In other words, we just add the same value each time ...

11.2 Arithmetic Sequences and Series - classzone.com

11.2 Arithmetic Sequences and Series 659 Arithmetic Sequences and Series USING ARITHMETIC SEQUENCES AND SERIES In an the difference between consecutive terms is constant. The constant difference is called the and is denoted by d. Identifying Arithmetic Sequences Decide whether each sequence is arithmetic. a.º3, 1, 5, 9, 13, . . . b.2, 5, 10 ...

3%2D5 Arithmetic Sequences as Linear Functions

The common difference between terms is ±3. So, to find the next term, subtract 3 from the last term. To find the next term, subtract 3 from the resulting number, and so on. 3 ± 3 = 0 0 ± 3 = ±3 ... Write the equation for the nth term of an arithmetic sequence with first term 8 and common difference 8. So, the function for this arithmetic ...

Arithmetic Sequences - Big Ideas Math

from real life. 3. In chemistry, water is called H ... How can you use an arithmetic sequence to describe a pattern? An arithmetic sequence is an ordered list of numbers in which the difference between each pair of consecutive terms, or numbers in the list, is the ... Writing the Terms of Arithmetic Sequences A sequence is an ordered list of ...

11.2 Arithmetic Sequences and Series - ClassZone

Page 1 of 2 11.2 Arithmetic Sequences and Series 661 The expression formed by adding the terms of an arithmetic sequence is called an The sum of the first n terms of an arithmetic series is denoted by S n.To find a rule for S n, you can write S n in two different ways and add the results. S n = a 1 + (a 1+ d)+ (a 1+ 2d)+. . . + a n

5.6 Arithmetic Sequences - Big Ideas Math

Section 5.6 Arithmetic Sequences 247 Help with Homework Use the ﬁ gures to complete the table. Then describe the pattern of the y-values. 3. n â 1 n â 2 n â 33 n â 4 Number of Quarters, n 1234 Number of Cents, y Write the next three terms of the arithmetic sequence.

Arithmetic Sequences and Partial Sums

Find a formula for an for the arithmetic sequence. 5. a1 = 15, d =4 6. a1 =−4, a5 =16 Find the sum of the finite arithmetic sequence. 7. Sum of the first 100 positive integers. 8. Sum of the integers from -100 to 30 Find the indicated nth partial sum of the arithmetic sequence. 9. 8, 20, 32, 44, …, n = 10 10.

9.2 Arithmetic Sequences and Partial Sums

Section 9.2 Arithmetic Sequences and Partial Sums 657 The sum of the first terms of an infinite sequence is the th partial sum. The th partial sum can be found by using the formula for the sum of a finite

10.3 Geometric Sequences and Series

1 Sec 10.3 Geometric Sequence and Series Learning Objectives: 1. Determine if a sequence is geometric. 2. Find a formula for the nth term of a geometric sequence. 3.

12.4 GEOMETRIC SEQUENCES AND SERIES

of the term preceding it, the nth term is given by an 6 1 3 n 1. EXAMPLE 2 Finding the nth term Find a formula for the nth term of the geometric sequence 2, 1, 1 2, 1 4, . . . . Solution We obtain the ratio by dividing a term by the term preceding it: r 1 2 1 2 Each term after the ﬁrst is obtained by multiplying the preceding term by 1 2. The ...

Geometric Sequences - projectmaths.ie

To enable students recognise a geometric sequence (geometric progression) • To enable students apply their knowledge of geometric sequences to everyday ... • Student Activities that accompany this Teaching and Learning Plan. Teaching & Learning Plan: Geometric Sequences

Using the Arithmetic Mean-Geometric Mean Inequality in ...

Using the Arithmetic Mean-Geometric Mean Inequality in Problem Solving by JIM WILSON A Presentation to the Annual Meeting of School Mathematics and Science Association, Birmingham, November 8, 2012, was prepared using some parts of this paper. PDF version The Arithmetic Mean-Geometric Mean Inequality (AM-GM Inquality) is a fundamental

2-2 Arithmetic and Geometric Series.ppt

geometric sequence, respectively. While it is possible to find a partial sum by writing down all of the terms and adding them up, it would easier to find a formula for Sn. ... Microsoft PowerPoint - 2-2 Arithmetic and Geometric Series.ppt [Compatibility Mode] Author:

Geometric or Arithmetic Mean: A Reconsideration

Geometric or Arithmetic Mean: A Reconsideration Eric Jacquier, Alex Kane, and Alan J. Marcus An unbiased forecast of the terminal value of a portfolio requires compounding of its initial lvalue ut its arithmetic mean return for the length of the investment period. Compounding at the arithmetic average historical

Arithmetic Sequences Date Period - WordPress.com

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Arithmetic Sequences - Beacon Learning Center

is an = a1 + (n – 1) d, where a1 is the first term and d is the common difference.” Derivation of arithmetic sequence: a1 a2 = a1 + d a3 = a2 + d = (a1 + d) + d = a1 + 2d a4 = a3 + d = (a1 + 2d) + d = a1 + 3d Examples: 1. Find the nth term of the arithmetic sequence 11, 2, -7… 2. The first term of an arithmetic sequence is –15 and the ...

SECTION 9.2: ARITHMETIC SEQUENCES and PARTIAL SUMS

(Chapter 9: Discrete Math) 9.14 PART C: FORMULA FOR THE nth PARTIAL SUM OF AN ARITHMETIC SEQUENCE The nthpartial sum of an arithmetic sequence with initial term a 1 and common difference d is given by: S n =n a 1 +a n 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Think: The (cumulative) sum of the first n terms of an arithmetic sequence is given by the number of terms involved times the average of the first and ...

Reteach x-x9-3 Arithmetic Sequences and Series (continued)

If you know any two terms in an arithmetic sequence, you can find any other term in the sequence. • Find the common difference by using the two terms and the formula for the nth term. • Then use the formula for the nth term to find the first term and the nth term. Find the 12th term of the arithmetic sequence with a 3 = 33 and a 9 = 117.

Basic Elements of Arithmetic Sequences and Series

UNIT G – GEOMETRIC SEQUENCES CLASS NOTES (COMPLETED – NO NEED TO COPY NOTES FROM OVERHEAD) Basic Elements of Arithmetic Sequences and Series Objective: • To establish basic elements of arithmetic sequences and series Example 1: Consider the arithmetic sequence 3, 7, 11, 15, 19, … What does the ‘…’ mean? What is the 7th term, t 7

8.3 Analyzing Geometric Sequences and Series

Section 8.3 Analyzing Geometric Sequences and Series 425 EEssential Questionssential Question How can you recognize a geometric sequence from its graph? In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant.For example, in the geometric sequence 1, 2, 4, 8, . . .

11.3 Geometric Sequences and Series - ClassZone

666 Chapter 11 Sequences and Series Geometric Sequences and Series USING GEOMETRIC SEQUENCES AND SERIES In a the ratio of any term to the previous term is constant. This constant ratio is called the and is denoted by r. Identifying Geometric Sequences Decide whether each sequence is geometric. a.1, 2, 6, 24, 120, . . . b.81, 27, 9, 3, 1 ...

ARITHMETIC AND GEOMETRIC PROGRESSIONS DEFINITION.

(iii) 7, 7, 7 is a constant geometric progression with three terms and the quotient between successive terms equal to 1. (iv) 2, 4, 8, 16, ::: is an in nite geometric progression with the quotient between successive terms equal to 2. TERMINOLOGY.Geometric progressions are sometimes called geometric sequences. A nite geometric progression with ...

Arithmetic and Geometric Series – Worksheet 1

Arithmetic and Geometric Series – Worksheet MCR3U Jensen General formula for an arithmetic series: ... If the first term of an arithmetic series is 2, the last term is 20, and the increase constant is +2 … a) Determine the number of terms in the series

Name: Date: Period: ARITHMETIC SEQUENCES & SERIES WORKSHEET

Name:_____ Date:_____ Period:_____ ARITHMETIC SEQUENCES & SERIES WORKSHEET The value of the nth term of an arithmetic sequence is given by the formula a n = a 1 + (n - 1)d where a 1 is the first term in the sequence, n is the position of the term in the sequence, and d is the common difference.

Arithmetic Sequences Date Period - Kuta Software LLC

Arithmetic Sequences Date_____ Period____ Determine if the sequence is arithmetic. ... Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. 7) a n ... = −9.2 Given a term in an arithmetic sequence and the common difference find the recursive formula and the

Arithmetic Sequences Quiz Review - Dutchess BOCES

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12.3 Geometric Sequences - YorkU Math and Stats

12.3 Geometric Sequences. 2 ... An infinite geometric series is a series of the form a + ar + ar2 + ar3 + ar4 + . . . + arn –1+ . . . We can apply the reasoning used earlier to find the sum of an infinite geometric series. The nth partial sum of such a series is given by the formula

LESSON Geometric Sequences 12-2 Practice and Problem ...

Practice and Problem Solving: A/B Each rule represents a geometric sequence. If the given rule is recursive, write it as an explicit rule. If the rule is explicit, write it as a recursive rule. Assume that f(1) is the first term of the sequence. 1. f(n) = 11(2)n−1 2.

9.3 Geometric Sequences and Series - OTHS Precal

Section 9.3 Geometric Sequences and Series 663 Geometric Sequences In Section 9.2, you learned that a sequence whose consecutive terms have a common difference is an arithmetic sequence. In this section, you will study another important type of sequence called a geometric sequence.

1 EXPLORATION: Recognizing Graphs of Geometric Sequences

Essential Question How can you recognize a geometric sequence from its graph? In a geometric sequence, the ratio of any term to the previous term, called the common ratio, is constant. For example, in the geometric sequence 1, 2, 4, 8, . . . , the common ratio is 2. Go to BigIdeasMath.com for an interactive tool to investigate this exploration.

Module 15: Geometric Sequences and Exponential Functions

including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Recognize that geometric sequences can be expressed as exponential functions. Construct exponential functions, including geometric sequences, given a

Arithmetic and Geometric Means - Kuta Software LLC

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Geometric Sequences Date Period - Kuta Software LLC

Given the first term and the common ratio of a geometric sequence find the first five terms and the explicit formula. 15) a 1 = 0.8 , r = −5 16) a 1 = 1, r = 2 Given the first term and the common ratio of a geometric sequence find the recursive formula and the three terms in the sequence after the last one given. 17) a 1 = −4, r = 6 18) a 1 ...

Geometric Average Versus Arithmetic Average

Suppose you invested in an emerging market mutual fund and earned 100% in year 1 and then lost 50% in year 2. What is your average annual return over the two-year period? The arithmetic average is clearly +25%, while if you plug in +1 for r1 and - .5 for r2 and then calculate the geometric average

How Many Recursive Calls Does a Recursive Function Make?

number and to track the number of recursive made to the defining function. Table 1 summarizes the output of the program. Quite evidently, the number of calls that function makes to itself grows much faster than n. Further, when n = 30, the program makes over 2.6x106 recursive calls. That is a tall

Recursive Definition: Recursive Functions

ambiguous recursive defs . problem to watch out for: recursive function on datum, e, is defined according to what constructor created e. If 2 or more ways to construct e, then which definition to use? recursivefunctions.29

Example 3 Arithmetic Prolog arithmetic expression examples ...

Prolog arithmetic expression examples & exercise. addition + multiplication * subtraction - division / power ^ mod mod In prolog 'is' has a special functionalityin evaluating arithmetic expressions. But with condition that the expression should be on the right side of 'is'otherwise it will

4.4 Monotone Sequences and Cauchy Sequences

4.4. MONOTONE SEQUENCES AND CAUCHY SEQUENCES 131 4.4 Monotone Sequences and Cauchy Sequences 4.4.1 Monotone Sequences The techniques we have studied so far require we know the limit of a sequence in order to prove the sequence converges. However, it is not always possible to –nd the limit of a sequence by using the de–nition, or the limit ...