Chapter 12.3, Problem 36AYU

To determine

To find: The $n\text{th}$ term of the geometric sequence.

Answer to Problem 36AYU

The $n\text{th}$ term is $a_n=\left(21\right){\left(\frac{1}{3}\right)}^{n-1}$ .

Explanation of Solution

Given information:

  $a_2=7$ and $r=\frac{1}{3}$ .

Calculation:

The first term of a sequence is denoted as $a_1$ and the second term of the sequence is denoted by $a_2$ .

The formula for nth term of geometric sequence is given by,

  $a_n=a_1{r}^{n-1}$

Calculate the first term by putting the values in above formula.

  $\begin{array}{l}7=\left(a_1\right){\left(\frac{1}{3}\right)}^{2-1}\\ a_1=\frac{7}{\left(\frac{1}{3}\right)}\\ a_1=21\end{array}$

Calculate the $n\text{th}$ term.

  $a_n=\left(21\right){\left(\frac{1}{3}\right)}^{n-1}$

Therefore, the $n\text{th}$ term of the sequence is $a_n=\left(21\right){\left(\frac{1}{3}\right)}^{n-1}$ .