Question

Write an equation for the nth term of each arithmetic sequence.

18, 11, 4, -3, ... .

Short answer

An equation for the nth term of the arithmetic sequence is$a_n=25-7n$ .

Step-by-step solution

Step 1. Given Information.

Given arithmetic sequence is 18, 11, 4, -3, ... .

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 $a_1=18$

The difference between the first two terms is $11-18=-7$

The difference between the next two terms is $4-11=-7$

Hence, the common difference is $d=-7$

Plugging the values in the formula:

$\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_n=18+(n-1)(-7)\\ a_n=18-7n+7\\ a_n=25-7n\end{array}$

Step 3. Conclusion.

Hence, an equation for the nth term of the arithmetic sequence is $a_n=25-7n$.