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

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Answer 1 · 2016-12-25T19:50:55

$a_12=-47$

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

$a_n=a_1+(n-1)d$

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

$a_n=8+(n-1)(-5)$
$a_n=8-5n+5$
$a_n=-5n+13$

To find $a_12$ (the 12th term), plug in $12$ for $n$ .

$a_12=-5(12)+13=-60+13=-47$

How do you find a_12a_12 given 8, 3, -2, ...?