Write an explicit formula for the sequence:

Question

Write an explicit formula for the sequence:

{-1/6 , 1/7, -1/8, 1/9, -1/10, 1/11, ...)

a_n= ?

Answer 1

Well the numerators start at 6 and increase by 1 each time, so in the nth term the numerator will be 5+n

The sign alternates so we must have a power of (-1) there.

So this will be (-1)ⁿ

So a_n = (-1)ⁿ (1/ (5+n))