# How do you find the 12th term of the arithmetic sequence 20, 14, 8, 2, -4, ...?

Dec 20, 2015

${12}^{t h}$ term$= - 46$

#### Explanation:

A term of an arithmetic sequence can be calculated with the formula:

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

where:
${t}_{\text{n}} =$any term in the arithmetic sequence
$a =$ first term
$n =$ term number/number of terms
$d =$ common difference

To find the ${12}^{t h}$ term of the sequence, we first need to find $d$, the common difference. We can do this by subtracting ${t}_{\text{1}}$ from ${t}_{\text{2}}$:

${t}_{\text{2"-t_"1}}$
$= 14 - 20$
$= - 6$

Now that you have the common difference, substitute all your known values into the formula to solve for ${t}_{\text{12}}$:

${t}_{\text{n}} = a + \left(n - 1\right) d$
${t}_{\text{12}} = 20 + \left(12 - 1\right) \left(- 6\right)$
${t}_{\text{12}} = 20 + \left(11\right) \left(- 6\right)$
${t}_{\text{12}} = 20 - 66$
${t}_{\text{12}} = - 46$

$\therefore$, the ${12}^{t h}$ term is $- 46$.