Chapter 11.3, Problem 15WE

To determine

To calculate:

The value of $t_6$ for following geometric sequence:

  $t_1=5,t_3=80$

Answer to Problem 15WE

The value of $t_6$ the geometric sequence is $5120$ .

Explanation of Solution

Given information:

  $t_1=5,t_3=80$

Formula used:

The $n^{th}$ term of geometric sequence is given by the following expression:

  $t_n=t_1{r}^{n-1}$

Where,

First term: $t_1$

Common difference: $r$

Calculation:

The value of common ratio is calculated as:

  $t_3=t_1{r}^{3-1}$

Put given values:

  $\begin{array}{l}80=\left(5\right)r^2\\ r^2=16\\ r=4\end{array}$

Now, the value of term $t_6$ is calculated as:

  $\begin{array}{l}{t}_6=t_1{r}^{6-1}\\ t_6=\left(5\right){\left(4\right)}^5\\ t_6=5120\end{array}$