Problem Solving

The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = a n-4 (subscript, comes at the bottom) for n > 4. What is the sum of the first 97 terms of the sequence?

A. 72
B. 74
C. 75
D. 78
E. 80

light_speed wrote:The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = a n-4 (subscript, comes at the bottom) for n > 4. What is the sum of the first 97 terms of the sequence?

A. 72
B. 74
C. 75
D. 78
E. 80

My answer would be B. 74

You are given a1, a2, a3, and a4. To get to B I summed a1-a4=3. There are four terms in a1-a4 1,2,3 and 4. 97/4=24 remainder 1. 24 x the sum of a1-a4 (3) = 72. There is still a remainder of 1 which represents a1. a1=2. 72+2=74 (B). I really dont know if that is the right answer or even if my method of solving the question is the right one. Maybe someone else can help.

K

I approached the same way Kaunteya did!

THanks
Senthil