Chapter 6.5, Problem 48E

To determine

To write:A sequence that has a pattern but is not arithmetic or geometric. Describe the pattern.

Answer to Problem 48E

The sequence $1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\mathrm{...}$ is neither the arithmetic nor the geometric. The general term of the sequence is $a_n=\frac{1}{n}$ .

Explanation of Solution

Giveninformation:

Not arithmetic or geometric sequence.

The sequence $1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\mathrm{...}$ is neither the arithmetic nor the geometric. Here, when you observe the denominators they are increased by 1. Also, the denominator value is same as the position of the term in the sequence. Therefore, the general term of the sequence is $a_n=\frac{1}{n}$ .