Q. 28

Find the first five terms of each arithmetic sequence described.

$a_{1} = \frac{5}{8}, d = \frac{3}{8}$

Verified

Answer

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

1Step 1. Given Information.

Given arithmetic sequence is described by $a_{1} = \frac{5}{8}, d = \frac{3}{8}$

2Step 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:

$\begin{matrix} a_{2} = a_{1} + d \\ a_{2} = \frac{5}{8} + \frac{3}{8} \\ a_{2} = \frac{8}{8} \\ a_{2} = 1 \end{matrix}$

The third term in the arithmetic sequence is:

$\begin{matrix} a_{3} = a_{2} + d \\ a_{3} = 1 + \frac{3}{8} \\ a_{3} = \frac{11}{8} \end{matrix}$

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:

$\begin{array}{l} a_{5} = a_{4} + d \\ a_{5} = \frac{7}{4} + \frac{3}{8} \\ a_{5} = \frac{17}{8} \end{array}$

3Step 3. Conclusion .

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