Derive the formula for the sum of a finite geometric series and use the formula to solve problems.

Sample Practice Questions (3)

The graph below shows the first three terms of a geometric sequence. Which value represents the sum of the first 10 terms of this sequence?

2, 046

1, 022

20

1, 024

Multiple choice · diagramSee Answer + Explanation →

Series A is defined by

a_{n} = 2 (3)^{n - 1}

for

n = 1

n = 5

. Series B is defined by

b_{n} = 3 (2)^{n - 1}

for

n = 1

n = 6

. Determine which series has a larger sum and justify your answer with calculations.

Open response · diagramSee Answer + Explanation →

The tape diagram below represents the first three terms of a geometric series. If the pattern continues, calculate the total length of the tape diagram after 6 terms.

Open response · diagramSee Answer + Explanation →

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More Algebra II Standards

NY-A.SSE.2-AIIUse the structure of an expression to identify ways to rewrite it. Apply to polynomial and rational expressions in the context of Algebra II.→NY-A.APR.2Know and apply the Remainder Theorem: for a polynomial p(x) and a number a the remainder on division by x - a is p(a). If p(a) = 0 then (x - a) is a factor of p(x).→NY-A.APR.3Identify zeros of polynomials when suitable factorizations are available and use the zeros to construct a rough graph of the function defined by the polynomial.→NY-A.APR.4Prove polynomial identities and use them to describe numerical relationships.→

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