Chapter 3, Problem 21PT

To determine

To find: $n^{th}$ term in the sequence.

Answer to Problem 21PT

Given sequence is Arithmetic.

  $n^{th}$ term of the sequence is $a_n=12n-7$ .

Explanation of Solution

Given information:

  $5,17,29,41,\mathrm{.....}$

Concept:

An Arithmetic sequence adds or subtracts a fixed amount (common difference) to get the next term in the sequence.

We know $n^{th}$ term of Arithmetic progression is

  $a_n=a+\left(n-1\right)d$

Where

  $a$ = First term

  $d$ = Common difference

Calculation:

Given series is

  $5,17,29,41,\mathrm{.....}$

Common difference = $d=17-5=29-17=41-29=12$

As difference between any two consecutive terms is same. So, the given series is Arithmetic.

From given sequence

First term = $a=5$

Common difference = $d=12$

Substituting values in $n^{th}$ term formula

We get

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ \Rightarrow a_n=5+\left(n-1\right)12\\ \Rightarrow a_n=5+12n-12\\ \Rightarrow a_n=12n-7\end{array}$

Therefore,

  $n^{th}$ term of the sequence is $a_n=12n-7$