Question

Find the first five terms of each arithmetic sequence described.

$a_1=5,d=3$

Short answer

The first five terms of the arithmetic sequence describedare 5, 8, 11, 14, 17.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is described by $a_1=5,d=3$

Step 2. Calculation.

In an arithmetic sequence a term can be obtained by adding the common difference to the previous term.

Here the first term is $a_1=5$

And, the common difference is $d=3$.

The second term in the arithmetic sequence is:

$\begin{array}{c}{a}_2=a_1+d\\ a_2=5+3\\ a_2=8\end{array}$

The third term in the arithmetic sequence is:

$\begin{array}{c}{a}_3=a_2+d\\ a_3=8+3\\ a_3=11\end{array}$

The fourth term in the arithmetic sequence is:

$\begin{array}{l}{a}_4=a_3+d\\ a_4=11+3\\ a_4=14\end{array}$

The fifth term in the arithmetic sequence is:

$\begin{array}{l}{a}_5=a_4+d\\ a_5=14+3\\ a_5=17\end{array}$

Step 3. Conclusion.

Hence, the first five terms of the arithmetic sequence described are 5, 8, 11, 14, 17.