Question

Find the first five terms of each arithmetic sequence described.

$a_1=\frac{4}{3},d=-\frac{1}{3}$

Short answer

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

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is described by $a_1=\frac{4}{3},d=-\frac{1}{3}$

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 $a_1=\frac{4}{3}$

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

The second term in the arithmetic sequence is:

$\begin{array}{c}{a}_2=a_1+d\\ a_2=\frac{4}{3}-\frac{1}{3}\\ a_2=1\end{array}$

The third term in the arithmetic sequence is:

$\begin{array}{c}{a}_3=a_2+d\\ a_3=1-\frac{1}{3}\\ a_3=\frac{2}{3}\end{array}$

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:

$\begin{array}{l}{a}_5=a_4+d\\ a_5=\frac{1}{3}-\frac{1}{3}\\ a_5=0\end{array}$

Step 3. Conclusion.

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