# Given an arithmetic sequence with d=-7 and a_7=4, what is a_22?

Jan 13, 2017

${a}_{22} = - 101$

#### Explanation:

${n}^{t h}$ term of an arithmetic sequence, whose first term is ${a}_{1}$ and common difference is $d$ is ${a}_{n} = {a}_{1} + \left(n - 1\right) d$.

As ${a}_{7} = {a}_{1} + \left(7 - 1\right) d = 4$, we have

${a}_{1} + 6 \times \left(- 7\right) = 4$

or ${a}_{1} = 4 + 42 = 46$

and hence ${a}_{22} = 46 + \left(22 - 1\right) \cdot \left(- 7\right)$

$= 46 - 21 \times 7$

$= 46 - 147$

$= - 101$