Modeling with Exponential and Logarithmic Equations

Question 1

Identify a1 and r for the sum of the geometric series. −4, 8, −16, 32,… a1 = r =

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Insufficient information

Question 2

r = [___]

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Insufficient information

Question 3

S6 = [___]

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84

Question 4

Find the sum.

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Answer image: //media.edgenuity.com/EVresources/3111-06-11-20-02-task/mc001-3.jpg

Question 5

a1 = [___]

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Part 1: 1/2; Part 2: 3/4; Part 3: 5; 1/2

Question 6

a1 = [___]d

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Part 1: 1/2; Part 2: 1/2; 0.5

Question 7

Write as a fraction in lowest terms:a =

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Part 1: 79; Part 2: 99; 79

Question 8

Which series represents this situation?

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1 + 1 · 7 + 1 · 72 + . . . 1 · 77

Question 9

How many curved triangles are in the ninth iteration? ⇒ 9841

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9841

Question 10

Explain why a geometric series with a ratio between zero and one converges and how you find the sum.

Revolt · Accepted Answer

A geometric series with a ratio between zero and one converges because its powers r^n approach zero as n becomes large. Using the finite sum formula S_n = a_1(1-r^n)/(1-r), the r^n term approaches zero, leaving the infinite sum S = a_1/(1-r).

Modeling with Exponential and Logarithmic Equations Answers

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