Chapter 11, Problem 2PT

To determine

To find the 25^th terms of an arithmetic sequence for which

  $a_1=9andd=5$

Answer to Problem 2PT

The 25^th terms of given arithmetic sequence is 129.

Explanation of Solution

Given:

  $a_1=9andd=5$

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 25^th terms of arithmetic sequence

  $a_1=9andd=5$

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 9 and common difference is

  $d=5$

To find 25^th terms of given sequence find $a_{25}$ , as

  $\begin{array}{c}{a}_{25}=9+\left(25-1\right)5\\ =9+\left(24\right)5\\ =9+120\\ =129\end{array}$

Thus, 25^th terms of given arithmetic sequence is 129.