# Given a_17=-82, d=-3, how do you find a_24?

Mar 2, 2017

${a}_{24} = - 93$

#### Explanation:

Find the first element of the sequence using the formula for arithmetic sequences: ${a}_{n} = {a}_{1} + \left(n - 1\right) d$

${a}_{17} = - 82 = {a}_{1} + \left(17 - 1\right) \left(- 3\right)$
$- 82 = {a}_{1} + 16 \left(- 3\right)$
$- 82 = {a}_{1} - 48$
$- 82 + 48 = {a}_{1} - 48 + 48$
${a}_{1} = - 82 + 48$
${a}_{1} = - 24$

Now use the arithmetic sequence formula to find ${a}_{24}$:

${a}_{24} = - 24 + \left(24 - 1\right) \left(- 3\right)$
${a}_{24} = - 24 + \left(23\right) \left(- 3\right)$
${a}_{24} = - 24 - 69$
${a}_{24} = - 93$