Chapter 12.3, Problem 6AYU

To determine

To find: The given statement is true or false.

Answer to Problem 6AYU

The given statement is true.

Explanation of Solution

Given information:

The given statement is.

For a geometric sequence with first term $a_1$ and common ratio $r$ ,where $r\ne 0$ , $r\ne 1$ , the sum of first $n$ terms is $S_n=a_1\cdot \frac{1-r^n}{1-r}$ .

Calculation:

A series in which the ratio of two consecutive term is constant is called geometric series.

The sum of first $n$ terms of the series is given by the formula.

  $S_n=a_1\cdot \frac{1-r^n}{1-r}$ .

Here $a_1$ is first term and $r$ is common ratio.

Therefore, the given statement is true.