Chapter 12.2, Problem 11CFU

To determine

To calculate:

The $1^{st}$ term of the geometric sequence is $r=2$ and $a_5=24$

Answer to Problem 11CFU

The $1^{st}$ term of the geometric sequence is $1.5$ .

Explanation of Solution

Given information:

  $\begin{array}{l}r=2\\ a_5=24\end{array}$

Formula used:

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

  $a_n=a_1{r}^{n-1}$

Calculation:

The $1^{st}$ term of the geometric sequence is calculated by using the $n^{th}$ term:

  $\begin{array}{l}{a}_5=a_1{r}^{5-1}\\ 24=a_1{\left(2\right)}^4\\ a_1=\frac{24}{16}\\ a_1=1.5\end{array}$