Question

Find the formula for the nth term of the arithmetic sequence -39, 61, 161, 261, ...

Answer 1

Given that it is arithmetic

$d = a_{2} - a_{1} = 61 - ( - 39) = 100$

$a_{n} = a_{1} + (n - 1)d \\ a_{n} = - 39+ 100 (n - 1) \\ a_{n} = - 39 + 100n - 100 \\ a_{n} = - 139 + 100n$