   Chapter 13.3, Problem 61E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# SKILLS59-64 ■ Partial Sums of a Geometric Sequence Find the sum. ∑ k = 1 6 5 ( − 2 ) k − 1

To determine

The partial sum of the geometric sequence.

Explanation

Given:

The partial sum of the geometric sequence is given as,

k=165(2)k1

Approach:

The partial sum of a geometric sequence is given as,

Sn=a1rn1r ……(1)

Here, Sn is the partial sum of nth term of the geometric sequence, n is the number of terms, a is the first term of the sequence and r is the common ratio of the sequence.

Calculation:

Calculate the first term from the given partial sum of the geometric sequence.

Substitute 1 for k to calculate the first term.

a1=5(2)11=5

Since the first term of the sequence is 5, the common ratio is (2) and the number of terms are 6

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