Question

Determine the nth term formula for each of the following sequences and find the limit if it exists.

3, 3,-3, 3,

Answer 1

aₙ = (-3) (-1)ⁿ⁻¹

limit does not exist

Explanation:

-3, 3, -3, 3, ...

This is an alternating geometric series where the first term is -3 and the common ratio is -1. The nth term is therefore:

aₙ = (-3) (-1)ⁿ⁻¹

Since the sequence alternates between -3 and 3, the limit as n approaches infinity of aₙ does not exist.