Counting Question

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light_speed: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Wed Jun 06, 2007 10:19 am

Counting Question

by light_speed » Sun Feb 24, 2008 7:36 pm

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

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Source: Beat The GMAT — Problem Solving | Sun Feb 24, 2008 7:36 pm

Kaunteya: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Mon Jan 28, 2008 4:12 pm; Location: Montreal, Canada; Thanked: 2 times

Re: Counting Question

by Kaunteya » Sun Feb 24, 2008 8:24 pm

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