Chapter 9, Problem 48RE

To determine

To find : an expression for the nth term of the geometric sequence and the 10th term of sequence.

Answer to Problem 48RE

  $a_n=5{\left(0.2\right)}^{n-1},a_{10}=0.00000256$

Explanation of Solution

Given information: $a_1=5,r=0.2$

Calculation:

The first term and geometric sequence are $a_1=5,r=0.2$ respectively.

The $n$ term of geometric sequence is

  $a_n=a_1{r}^{n-1}$

By substituting, the values of $a_1$ and r , we get

  $a_n=5{\left(0.2\right)}^{n-1}$

Now, 10^th term of the sequence is

  $\begin{array}{l}{a}_{10}=5{\left(0.2\right)}^9\\ a_{10}=0.00000256\end{array}$