Question

Find the first five terms of each arithmetic sequence described.

$a_1=6,d=-4$

Short answer

The first five terms of the arithmetic sequence described are6, 2, -2, -6, -10.

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is described by $a_1=6,d=-4$

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 $a_1=6$

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

The second term in the arithmetic sequence is:

$\begin{array}{c}{a}_2=a_1+d\\ a_2=6-4\\ a_2=2\end{array}$

The third term in the arithmetic sequence is:

$\begin{array}{c}{a}_3=a_2+d\\ a_3=2-4\\ a_3=-2\end{array}$

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:

$\begin{array}{l}{a}_5=a_4+d\\ a_5=-6-4\\ a_5=-10\end{array}$

Step 3. Conclusion.

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