Chapter 11, Problem 3PT

To determine

What is the 8^th terms of arithmetic sequence that begins

  $18,20.2,22.4,\mathrm{24.6......}$

Answer to Problem 3PT

The 8^th terms of given arithmetic sequence is 33.4.

Explanation of Solution

Given:

  $18,20.2,22.4,\mathrm{24.6......}$

Concept Used:

  $n^{th}$ term of an arithmetic sequence with first term a and common term d is: $a_n=a_{\left(n-1\right)}+d$ .

Calculation:

In order to find the 8^th terms of arithmetic sequence

  $18,20.2,22.4,\mathrm{24.6......}$

Use the formula for $n^{th}$ term of an arithmetic sequence with first term a and common term d is: $a_n=a+\left(n-1\right)d$ .

Here, given that first term is 18 and common difference is

  $\begin{array}{c}d=a_2-a_1\\ =20.2-18\\ =2.2\end{array}$

To find next 8^th of given sequence find $a_8$ , as

  $\begin{array}{c}{a}_8=18+\left(8-1\right)2.2\\ =18+\left(7\right)2.2\\ =18+15.4\\ =33.4\end{array}$

Thus, 8^th terms of given arithmetic sequence is 33.4.