Chapter 8, Problem 3RE

To determine

To find: an expression for the nth term of the given arithmetic sequence.

Answer to Problem 3RE

An expression for the nth term of the arithmetic sequence is $a_n=2+5n$ .

Explanation of Solution

Given information:

An sequence is given as $7,12,17,22,27,\mathrm{...}$ .

Calculation:

Now, consider the given sequence.

  $7,12,17,22,27,\mathrm{...}$

Consider dbe the common difference and $a_1$ as the first term.

  $\begin{array}{l}{a}_1=7\\ d=a_2-a_1=12-7=5\end{array}$

So, the nth term of the arithmetic sequence can be found as

  $\begin{array}{c}{a}_n=a_1+\left(n-1\right)d\\ =7+\left(n-1\right)\left(5\right)\\ =7+5n-5\\ =2+5n\end{array}$

Thus, the expression for the nth term of the arithmetic sequence is $a_n=2+5n$ .