Question

Find the first five terms of each arithmetic sequence described.

$a_1=2,d=13$

Short answer

The first five terms of the arithmetic sequence described are2, 15, 28, 41, 54.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is described by $a_1=2,d=13$.

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 $a_1=2$

And, the common difference is $d=13$.

The second term in the arithmetic sequence is:

$\begin{array}{c}{a}_2=a_1+d\\ a_2=2+13\\ a_2=15\end{array}$

The third term in the arithmetic sequence is:

$\begin{array}{c}{a}_3=a_2+d\\ a_3=15+13\\ a_3=28\end{array}$

The fourth term in the arithmetic sequence is:

$\begin{array}{l}{a}_4=a_3+d\\ a_4=28+13\\ a_4=41\end{array}$

The fifth term in the arithmetic sequence is:

$\begin{array}{l}{a}_5=a_4+d\\ a_5=41+13\\ a_5=54\end{array}$

Step 3. Conclusion.

Hence, the first five terms of the arithmetic sequence described are 2, 15, 28, 41, 54.