Chapter 12.3, Problem 23AYU

In Problems 19-26, find the fifth term and the $n^{\text{th}}$ term of the geometric sequence whose initial term $a_1$ and common ratio $r$ are given.

$a_1=0;r=\frac{1}{2}$

To determine

To find: To calculate the fifth term and the nth term of the geometric sequence using the given first term and common ratio.

Answer to Problem 23AYU

Solution:

The $n^{th}$ term of the geometric sequence is $a_n=0$ and the fifth term value is $a_5=0$.

Explanation of Solution

Given:

The first term $a_1=0$ and the common ratio $r=\frac{1}{2}$.

Formula used:

The $n^{th}$ term of the geometric sequence is

$a_n=a_1\cdot r^{n-1}$

$a_n=0\cdot {\left(\frac{1}{2}\right)}^{n-1}=0$

The fifth term of the geometric sequence is $a_5=0\cdot {\left(\frac{1}{2}\right)}^4=0\times \frac{1}{16}=0$.