Q. 23

Find the first five terms of each arithmetic sequence described.

$a_{1} = 2, d = 13$

Verified

Answer

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

1Step 1. Given Information.

Given arithmetic sequence is described by $a_{1} = 2, d = 13$ .

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 $a_{1} = 2$

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

The second term in the arithmetic sequence is:

$\begin{matrix} a_{2} = a_{1} + d \\ a_{2} = 2 + 13 \\ a_{2} = 15 \end{matrix}$

The third term in the arithmetic sequence is:

$\begin{matrix} a_{3} = a_{2} + d \\ a_{3} = 15 + 13 \\ a_{3} = 28 \end{matrix}$

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:

$\begin{array}{l} a_{5} = a_{4} + d \\ a_{5} = 41 + 13 \\ a_{5} = 54 \end{array}$

3Step 3. Conclusion .

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