Chapter 9.2, Problem 21E

To determine

To Find: The formula for $a_n$ for the arithmetic sequence.

Answer to Problem 21E

The $n^{th}$ term of the sequence is $a_n=3n-2$ .

Explanation of Solution

Given information:

  $a=1\&d=3$

Concept and Formula Used:

A sequence is airthmetic when the differences between consecutive terms are the same.

General term of the sequence: $a_n=a+\left(n-1\right)d$

where $a$ is the first term and $d$ is the common difference.

Calculation:

It is given that $a=1\&d=3$

Using the formula for $n^{th}$ term

  $\begin{array}{l}{a}_n=a+\left(n-1\right)d\\ a_n=1+\left(n-1\right)3\\ a_n=1+3n-3\\ a_n=3n-2\end{array}$

Conclusion:

The $n^{th}$ term of the sequence is $a_n=3n-2$ .