Question

Find the first five terms of each arithmetic sequence described.

$a_1=\frac{5}{8},d=\frac{3}{8}$

Short answer

The first five terms of the arithmetic sequence described are$\frac{5}{8},1,\frac{11}{8},\frac{7}{4},\frac{17}{8}$ .

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is described by $a_1=\frac{5}{8},d=\frac{3}{8}$

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 $a_1=\frac{5}{8}$

And, the common difference is$d=\frac{3}{8}$ .

The second term in the arithmetic sequence is:

$\begin{array}{c}{a}_2=a_1+d\\ a_2=\frac{5}{8}+\frac{3}{8}\\ a_2=\frac{8}{8}\\ a_2=1\end{array}$

The third term in the arithmetic sequence is:

$\begin{array}{c}{a}_3=a_2+d\\ a_3=1+\frac{3}{8}\\ a_3=\frac{11}{8}\end{array}$

The fourth term in the arithmetic sequence is:

$\begin{array}{l}{a}_4=a_3+d\\ a_4=\frac{11}{8}+\frac{3}{8}\\ a_4=\frac{14}{8}\\ a_4=\frac{7}{4}\end{array}$

The fifth term in the arithmetic sequence is:

$\begin{array}{l}{a}_5=a_4+d\\ a_5=\frac{7}{4}+\frac{3}{8}\\ a_5=\frac{17}{8}\end{array}$

Step 3. Conclusion.

Hence, the first five terms of the arithmetic sequence described are $\frac{5}{8},1,\frac{11}{8},\frac{7}{4},\frac{17}{8}$.