Chapter 3, Problem 53SGR

To determine

To find: $n^{th}$ term of arithmetic sequence.

Answer to Problem 53SGR

  $a_n=5n+1$

Explanation of Solution

Given information:

  $\begin{array}{l}{a}_1=6\\ d=5\end{array}$

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

  $a_n=a_1+\left(n-1\right)d$

Where

  $a_1$ = First term

  $d$ = Common difference

Calculation:

Given

  $\begin{array}{l}{a}_1=6\\ d=5\end{array}$

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

We get

  $\begin{array}{l}{a}_n=a_1+\left(n-1\right)d\\ \Rightarrow a_n=6+\left(n-1\right)5\\ \Rightarrow a_n=6+5n-5\\ \Rightarrow a_n=5n+1\end{array}$

Therefore,

  $n^{th}$ term of Arithmetic sequence is $a_n=5n+1$