# Chapter 22: Chapter 22

Problem 688

Find the sum of the first eight terms of the geometric progression: $4,-4 / 3,4 / 9,-4 / 27$

Problem 689

Sum the sequence \(2 / 3,-1,3 / 2, \ldots \ldots\) to 7 term.

Problem 690

Find the sum of the first six terms of a geometric progression whose first term is \(1 / 3\) and whose second term is \(-1\).

Problem 691

Find the seventh term of a geometric series whose third term is \(1 / 8\) and common ratio is \(2 .\) Find the first seven terms.

Problem 695

Insert three geometric mean between 16 and 81 .

Problem 696

Find the first four terms of the geometric progression generated by the exponential function \(\mathrm{f}(\mathrm{x})=12(3 / 2)^{\mathrm{x}}\) if the domain of the function is the set of nonnegative integers \((0,1,2,3, \ldots)\)

Problem 697

Find three numbers in geometric progression whose sum is 19, and whose product is 216 .

Problem 698

Express \(.423\) as a rational fraction.

Problem 699

A person has 2 parents, 4 grandparents, 8 greatgrandparents, and so on. Find the number of his ancestors during the eight generations preceding his own, provided there are no duplications.

Problem 700

If \(\mathrm{x}<1\), sum the series $1+2 \mathrm{x}+3 \mathrm{x}^{2}+4 \mathrm{x}^{3}+\ldots$ to infinity.