Q. 27

Find the first five terms of each arithmetic sequence described.

$a_{1} = \frac{4}{3}, d = - \frac{1}{3}$

Verified

Answer

The first five terms of the arithmetic sequence described are $\frac{4}{3}, 1, \frac{2}{3}, \frac{1}{3}, 0$ .

1Step 1. Given Information.

Given arithmetic sequence is described by $a_{1} = \frac{4}{3}, d = - \frac{1}{3}$

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 $a_{1} = \frac{4}{3}$

And, the common difference is $d = - \frac{1}{3}$ .

The second term in the arithmetic sequence is:

$\begin{matrix} a_{2} = a_{1} + d \\ a_{2} = \frac{4}{3} - \frac{1}{3} \\ a_{2} = 1 \end{matrix}$

The third term in the arithmetic sequence is:

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

The fourth term in the arithmetic sequence is:

$\begin{array}{l} a_{4} = a_{3} + d \\ a_{4} = \frac{2}{3} - \frac{1}{3} \\ a_{4} = \frac{1}{3} \end{array}$

The fifth term in the arithmetic sequence is:

$\begin{array}{l} a_{5} = a_{4} + d \\ a_{5} = \frac{1}{3} - \frac{1}{3} \\ a_{5} = 0 \end{array}$

3Step 3. Conclusion .

Hence, the first five terms of the arithmetic sequence described are $\frac{4}{3}, 1, \frac{2}{3}, \frac{1}{3}, 0$ .