Chapter 12, Problem 34RE

To determine

To find: The indicated term of the given sequence.

Answer to Problem 34RE

The $11\text{th}$ term is $1024$ .

Explanation of Solution

Given:

The given sequence is,

  $1,2,4,\mathrm{8....}$

The term to be determined is $n=11$ .

Calculation:

Consider the given sequence is,

  $1,2,4,\mathrm{8....}$

Consider the common ratio of the sequence is,

  $\begin{array}{c}\frac{a_2}{a_1}=\frac{2}{1}\\ =2\end{array}$

Consider the general form of the geometric sequence is,

  $a_n=a_1{r}^{n-1}$

Then, the 11 th term is,

  $\begin{array}{c}{a}_{11}=\left(1\right){\left(2\right)}^{11-1}\\ =1024\end{array}$

Thus, the $11\text{th}$ term is $1024$ .