Chapter 12, Problem 19RE

To determine

To find:The ninth term of given sequence.

Answer to Problem 19RE

The ninth term of given sequence is $9\sqrt{2}$ .

Explanation of Solution

Given information:

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

Calculation:

The sequence is,

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

The common difference is,

  $\begin{array}{c}{d}_1=2\sqrt{2}-\sqrt{2}\\ =\sqrt{2}\\ d_2=3\sqrt{2},-2\sqrt{2}\\ =\sqrt{2}\end{array}$

Since, the common difference is same.

Thus, the sequence is arithmetic.

The ninth term is,

  $\begin{array}{c}{a}_9=\sqrt{2},+\left(9-1\right)\sqrt{2},\\ =\sqrt{2},+8\sqrt{2}\\ =9\sqrt{2}\end{array}$