sequence problem

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zagcollins: Master | Next Rank: 500 Posts; Posts: 167; Joined: Wed Jun 11, 2008 10:58 pmFollowed by: 1 member; Thanked: 2 times

by zagcollins » Mon Jul 14, 2008 8:35 am

The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 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 | Mon Jul 14, 2008 8:35 am

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: sequence problem

by Ian Stewart » Mon Jul 14, 2008 8:45 am

zagcollins wrote:The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 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

If an = an-4 for all n greater than 4, then a5 = a1, a6 = a2, a7 = a3, a8 = a4, a9 = a5 = a1, etc. So the sequence is just:

2, -3, 5, -1, 2, -3, 5, -1, 2, -3, 5, -1 ....

This repeats in blocks of four. The sum of the first four terms is 3. If we add the first 96 terms, we'll just be adding that same block of four terms 24 times; the sum will be 24*3 = 72. If we add on the 97th term, which will be 2, we get the final answer: 72 + 2 = 74.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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sudhir3127: Legendary Member; Posts: 829; Joined: Mon Jul 07, 2008 10:09 pmFollowed by: 3 members; Location: INDIA; Thanked: 84 times

by sudhir3127 » Mon Jul 14, 2008 10:07 am

nice explanation Ian.. i actually thought it an - 4 rather its an-4( as in a base (n-4))

thanks for the answer.

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Thu Jan 21, 2010 10:24 pm

fantastic explanation Ian

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sreak1089: Master | Next Rank: 500 Posts; Posts: 379; Joined: Wed Jun 03, 2009 3:05 amFollowed by: 1 member; Thanked: 19 times; GMAT Score:690

by sreak1089 » Thu Jan 21, 2010 10:52 pm

I too thought as below. But, once I saw a part of explanation from I realized that it is meant to be base (n-4). Then it was easy to solve

sudhir3127 wrote:nice explanation Ian.. i actually thought it an - 4 rather its an-4( as in a base (n-4))

thanks for the answer.

Like this post

sreak1089: Master | Next Rank: 500 Posts; Posts: 379; Joined: Wed Jun 03, 2009 3:05 amFollowed by: 1 member; Thanked: 19 times; GMAT Score:690

by sreak1089 » Thu Jan 21, 2010 10:52 pm

I too thought the same thing and was confused. The moment I realized that it was meant to be base(n-4), it was easy to solve

sudhir3127 wrote:nice explanation Ian.. i actually thought it an - 4 rather its an-4( as in a base (n-4))

thanks for the answer.

Like this post

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