Chapter 11.3, Problem 34SR

To determine

To find: The first five terms of geometric sequence.

Answer to Problem 34SR

The first five terms are $4$ , $2$ , $1$ , $0.5$ , and $0.25$ .

Explanation of Solution

Given:

It is given that $a_1=4,r=0.5$ .

Calculation:

The formula for geometric sequence is given by $a_n=a_1{r}^{n-1}$ .

Substitute 4 for $a_1$ , $0.5$ for $r$ and $2$ for $n$ in the formula $a_n=a_1{r}^{n-1}$ to find the second term.

  $\begin{array}{c}{a}_2=4{\left(0.5\right)}^{2-1}\\ =2\end{array}$

Substitute 4 for $a_1$ , $0.5$ for $r$ and 3 for $n$ in the formula $a_n=a_1{r}^{n-1}$ to find the third term.

  $\begin{array}{c}{a}_3=4{\left(0.5\right)}^{3-1}\\ =1\end{array}$

Substitute 4 for $a_1$ , $0.5$ for $r$ and 4 for $n$ in the formula $a_n=a_1{r}^{n-1}$ to find the fourth term.

  $\begin{array}{c}{a}_4=4{\left(0.5\right)}^{4-1}\\ =0.5\end{array}$

Substitute 4 for $a_1$ , $0.5$ for $r$ and 5 for $n$ in the formula $a_n=a_1{r}^{n-1}$ to find the fifth term.

  $\begin{array}{c}{a}_5=4{\left(0.5\right)}^{5-1}\\ =0.25\end{array}$

Therefore, the first five terms are $4$ , $2$ , $1$ , $0.5$ , and $0.25$ .