Chapter 14.7, Problem 3MRE

To determine

To find:Whether the sequence is arithmetic or geometric and then find the specified term of the sequence.

Answer to Problem 3MRE

The given series is a geometric progression and it ${11}^{\text{th}}$ term is $9216$ .

Explanation of Solution

Given: $9,18,36,\mathrm{.......},t_{11}$ .

Check from common difference.

  $\begin{array}{c}18-9=36-18\\ 9\ne 18\end{array}$

The common difference is not same. So, the sequence is not an arithmetic progression.

Check for common ratio.

  $\begin{array}{c}\frac{18}{9}=\frac{36}{18}\\ 2=2\end{array}$

The common ratio is same. So, the sequence is a geometric progression.

The expression for the $n^{\text{th}}$ term of angeometric sequence is given by.

  $a_n=a{r}^{n-1}$

Substitute the values in the above expression.

  $\begin{array}{c}{a}_{11}=\left(9\right)2^{11-1}\\ =9216\end{array}$

Therefore, the given series is ageometric progression and it ${11}^{\text{th}}$ term is $9216$ .