Question

Find the eighteenth term of a sequence where the first term is 13 and the common difference is −7.

Short answer

-106

Step-by-step solution

Step 1. Given Information.

The first term is 13 and the common difference is -7.

Step 2. Formula used.

Write the formula of an arithmetic sequence.

$a_n=a_1+\left(n-1\right)d$

Wherea₁ is the first term andd is a common difference.

Step 3. Find the eighteenth term. 

Substitute 7 for the first term, 9 for d, and 18 for thenabove formula.

$\begin{array}{rcl}{a}_{18}& =& 13+\left(18-1\right)\left(-7\right)\\ & =& 13-119\\ & =& -106\end{array}$