It would help to know what you have been learning.
But I suspect they want you to think about what [MATH]a_n[/MATH] would be if [MATH]a_{n+1} = a_n[/MATH]. How would that relate to a possible limit?
Once you have a candidate for the limit, you can try proving it.
EDIT: afos's idea is essentially equivalent to this, and a little more formal.