Q. 25

Find the first five terms of each arithmetic sequence described.

$a_{1} = 6, d = - 4$

Verified

Answer

The first five terms of the arithmetic sequence described are 6, 2, -2, -6, -10.

1Step 1. Given Information.

Given arithmetic sequence is described by $a_{1} = 6, d = - 4$

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 $a_{1} = 6$

And, the common difference is $d = - 4$ .

The second term in the arithmetic sequence is:

$\begin{matrix} a_{2} = a_{1} + d \\ a_{2} = 6 - 4 \\ a_{2} = 2 \end{matrix}$

The third term in the arithmetic sequence is:

$\begin{matrix} a_{3} = a_{2} + d \\ a_{3} = 2 - 4 \\ a_{3} = - 2 \end{matrix}$

The fourth term in the arithmetic sequence is:

$\begin{array}{l} a_{4} = a_{3} + d \\ a_{4} = - 2 - 4 \\ a_{4} = - 6 \end{array}$

The fifth term in the arithmetic sequence is:

$\begin{array}{l} a_{5} = a_{4} + d \\ a_{5} = - 6 - 4 \\ a_{5} = - 10 \end{array}$

3Step 3. Conclusion .

Hence, the first five terms of the arithmetic sequence described are 6, 2, -2, -6, -10.