Chapter 9.8, Problem 38HP

To determine

To evaluate: the sequence of numbers that form a pattern but are neither arithmetic nor geometric.

Answer to Problem 38HP

  $1,1,1,1,\mathrm{1......}$ is the sequence which is both arithmetic and geometric.

Explanation of Solution

Given:

Haro and Mathew are finding the ninth term of the geometric sequence −5, 10, −20 …

Any sequence that has each term same, is both geometric and arithmetic.

For example,

  $1,1,1,1,\mathrm{1......}$

In the above sequence, common difference is 0 therefore it is arithmetic sequence and common ratio is 1 therefore it is geometric sequence.