Question

Find the fourteenth term of a sequence where the first term is eight and the common difference is −3.

Short answer

-31

Step-by-step solution

Step 1. Given Information. 

The first term is eight and the common difference is −3.

Step 2. Formula used.

Write the formula of an arithmetic sequence.

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

Where a₁ is the first term and d is a common difference.

Step 3. Find the fourteenth term. 

Substitute 8 for the first term, -3 for d, and 14 for nin the above formula.

$\begin{array}{rcl}{a}_{14}& =& 8+\left(14-1\right)\left(-3\right)\\ & =& 8+\left(13\right)\left(-3\right)\\ & =& 8-39\\ & =& -31\end{array}$