Chapter 12, Problem 35RE

To determine

To find: The indicated term of the given sequence.

Answer to Problem 35RE

The $9\text{th}$ term is $9\sqrt{2}$ .

Explanation of Solution

Given:

The given sequence is,

  $\sqrt{2},2\sqrt{2},3\sqrt{2}\mathrm{.....}$

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

Calculation:

Consider the given sequence is,

  $\sqrt{2},2\sqrt{2},3\sqrt{2}\mathrm{.....}$

Consider the common difference of the sequence is,

  $\begin{array}{c}d=2\sqrt{2}-\sqrt{2}\\ =\sqrt{2}\end{array}$

Consider the general form of the arithmetic sequence is,

  $a_n=a_1+\left(n-1\right)d$

Then, the 9th term is,

  $\begin{array}{c}{a}_9=\sqrt{2}+\left(9-1\right)\sqrt{2}\\ =9\sqrt{2}\end{array}$

Thus, the $9\text{th}$ term is $9\sqrt{2}$ .