Chapter 3, Problem 4PFA

To determine

To find:Equation for $n^{th}$ term of the sequence

Answer to Problem 4PFA

  $a_n=7n-19$

Explanation of Solution

Given information:

First four term of sequence are $-12,-5,2,9$ .

Concept used:

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

  $a_n=a+\left(n-1\right)d$

Where

  $a$ = first term.

  $d$ = common difference.

  $n$ = number of terms.

  $-12,-5,2,9$ are first four terms of sequence.

Here

First term = $a=-12$

Common difference = $d=-5-\left(-12\right)=2-\left(-5\right)=9-2=7$

  $\Rightarrow d=7$

On substituting values in formula

We get

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ \Rightarrow a_n=-12+\left(n-1\right)7\\ \Rightarrow a_n=-12+7n-7\\ \Rightarrow a_n=7n-19\end{array}$

Therefore, $n^{th}$ term of sequence is $a_n=7n-19$