Chapter 9, Problem 47RE

To determine

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

Answer to Problem 47RE

  $a_n=100{\left(1.05\right)}^{n-1},a_{10}=100{\left(1.05\right)}^9$

Explanation of Solution

Given information: $a_1=100,r=1.05$

Calculation:

The first term and geometric sequence are $a_1=100,r=1.05$ 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

  $a_n=100{\left(1.05\right)}^{n-1}$

Now, 10^th term of the sequence is

  $a_{10}=100{\left(1.05\right)}^9$