# How do you find a_12 given 8, 3, -2, ...?

Dec 25, 2016

${a}_{12} = - 47$

#### Explanation:

Find ${a}_{12}$ given $8 , 3 , - 2. . .$

Note that each term is 5 less than the previous term. This implies that the sequence is arithmetic and of the form

${a}_{n} = {a}_{1} + \left(n - 1\right) d$

where ${a}_{1}$ is the first term and $d$ is the common difference between the terms.

In this example ${a}_{1} = 8$ and $d = - 5$

The "formula" for this sequence is then

${a}_{n} = 8 + \left(n - 1\right) \left(- 5\right)$
${a}_{n} = 8 - 5 n + 5$
${a}_{n} = - 5 n + 13$

To find ${a}_{12}$ (the 12th term), plug in $12$ for $n$.

${a}_{12} = - 5 \left(12\right) + 13 = - 60 + 13 = - 47$