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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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

SKILLS

53-58 ■ Partial Sums of a Geometric Sequence Find the sum.

5120 + 2560 + 1280 + + 20

To determine

The partial sum of the geometric sequence.

Explanation

Given:

The partial sum of the geometric sequence is given as,

5120+2560+1280++20

Approach:

The nth term of the geometric sequence is given as,

an=arn1 ……(1)

Here, an is the nth term of the geometric sequence.

The partial sum of a geometric sequence is given as,

Sn=a1rn1r ……(2)

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:

Since the first term of the sequence is 5120 and the common ratio is 12. Then,

Calculate the term of the geometric sequence.

Substitute 5120 for a, 12 for r and 20 for an in equation (1) to calculate the term of the sequence.

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