Question

Write an equation for the nth term of the arithmetic sequence -26, -15, -4, 7, ... .

Short answer

An equation for the nth term of the arithmetic sequence is $a_n=11n-37$ .

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is -26, -15, -4, 7, ....

Step 2. Calculation.

The n^th term of an arithmetic sequence is given by$a_n=a_1+(n-1)d$ .

Here the first term is$a_1=-26$

The difference between the first two terms is $(-15)-(-26)=-15+26=11$

The difference between the next two terms is $(-4)-(-15)=-4+15=11$

Hence, the common difference is $d=11$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=-26+(n-1)\left(11\right)\\ a_n=-26+11n-11\\ a_n=11n-37\end{array}$

Step 3. Conclusion.

Hence, an equation for the nth term of the arithmetic sequence is $a_n=11n-37$.