Chapter 12.3, Problem 72AYU

To determine

To verify whether the given sequence is arithmetic, geometric or neither. If the sequence is arithmetic or geometric, find the common difference or common ratio accordingly and calculate the sum of the first 50 terms.

Answer to Problem 72AYU

The given sequence is neither arithmetic nor geometric.

Explanation of Solution

Given:

Sequence is given as $\left\{5n^2+1\right\}$. Considering the values of $n$ as a positive integers, the sequence becomes $6,21,46,81,\cdots$.

There is no common difference and common ratio for the given sequence.

Therefore, the sequence $\left\{5n^2+1\right\}$ is neither arithmetic nor geometric.