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

3, 3,-3, 3,

aₙ = (-3) (-1) ⁿ⁻¹

limit does not exist

Step-by-step 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.