Chapter 12, Problem 33RE

To determine

To find: The indicated term of the given sequence.

Answer to Problem 33RE

The $11\text{th}$ term is $\frac{1}{{10}^{10}}$ .

Explanation of Solution

Given:

The given sequence is,

  $1,\frac{1}{10},\frac{1}{100}\mathrm{.....}$

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

Calculation:

Consider the given sequence is,

  $1,\frac{1}{10},\frac{1}{100}\mathrm{.....}$

Consider the common ratio of the sequence is,

  $\begin{array}{c}\frac{a_2}{a_1}=\frac{\frac{1}{10}}{1}\\ =\frac{1}{10}\end{array}$

Consider the general form of the geometric sequence is,

  $a_n=a_1{r}^{n-1}$

Then, the 11 th term is,

  $\begin{array}{c}{a}_{11}=\left(1\right){\left(\frac{1}{10}\right)}^{11-1}\\ =\frac{1}{{10}^{10}}\end{array}$

Thus, the $11\text{th}$ term is $\frac{1}{{10}^{10}}$ .