Question

Find the first five terms of each arithmetic sequence described.
$a_1=12,d=-3$

Short answer

The first five terms of the arithmetic sequence describedare12, 9, 6, 3, 0.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is described by $a_1=12,d=-3$

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 $a_1=12$

And, the common difference is$d=-3$ .

The second term in the arithmetic sequence is:

$\begin{array}{c}{a}_2=a_1+d\\ a_2=12-3\\ a_2=9\end{array}$

The third term in the arithmetic sequence is:

$\begin{array}{c}{a}_3=a_2+d\\ a_3=9-3\\ a_3=6\end{array}$

The fourth term in the arithmetic sequence is:

$\begin{array}{l}{a}_4=a_3+d\\ a_4=6-3\\ a_4=3\end{array}$

The fifth term in the arithmetic sequence is:

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

Step 3. Conclusion.

Hence, the first five terms of the arithmetic sequence described are 12, 9, 6, 3, 0.