Sequence Math Problem

Question

A certain sequence begins with the terms 4,-4,-1,5,-1,4,-4,-1,5,-1,4,-4,-1,5,-1.... and continues to repeat indefinitely. What is the sum of the first 81 terms of the sequence?

Answer 1

First, find the pattern: the sequence repeats 4,-4,-1,5,-1 with sum 4-4-1+5-1 = 3. Now, 5 divides 81 with a remainder of 1. Thus, the sum of the first 80th terms must be (80/5)*3 = 16*3 = 48, and so the sum of the first 81 terms is 48+4 = 52.