   Chapter 13.CR, Problem 63E ### 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

# Ancestors A person has two parents, four grandparents, eight great-grandparents, and so on. What is the total number of a person’s ancestors in 15 generations?

To determine

To find:

The total number of a person’s ancestors in 15 generations.

Explanation

Given:

A person has two parents, four grandparents, eight great-grandparents, and so on.

Approach:

Show that the number of ancestors in subsequent generations form a geometric sequence. And find partial sum of first 15 terms of this generation.

Calculation:

Ratio of ancestors in second generation to first generation is 42=2.

Ratio of ancestors in third generation to second generation is 84=2.

This proves that the ancestors in subsequent generation form a geometric sequence with first term, a=2 and common ratio, r=2.

The sum of first 15 terms of this sequence is,

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