# What is the 41st term of the arithmetic sequence where a1 = 17 and a15 = –39 ?

Nov 26, 2015

$- 143$

#### Explanation:

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

${a}_{15} = {a}_{1} + 14 r$

$- 39 = 17 + 14 r$

$- 56 = 14 r$

$- 4 = r$

${a}_{41} = {a}_{1} + 40 r = 17 - 4 \cdot 40$