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Sum of Sequences

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by HarvardDreamin » Sat Mar 22, 2008 9:48 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 in this sequence?

a) 72 b 74 c) 75 d) 78 e)80
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by madhavi » Sun Mar 23, 2008 6:27 am
Can you please confirm what is an? Is an = a(n-4)th term??
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by simplyjat » Sun Mar 23, 2008 6:40 am
Whats your issue with the question, its a simple and straight question...
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by HarvardDreamin » Sun Mar 23, 2008 10:05 am
an is the same as a to the nth term
simplyjat wrote:Whats your issue with the question, its a simple and straight question...
Can you show me how to solve it ?

Thanks
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by madhavi » Sun Mar 23, 2008 10:15 am
From my understanding,

a1=2
a2=-3
a3=5
a4=1
a5= a(5-4)=a1=2
a6=a2=-3...

So every set of four elements in a row are the same and sum upto 5.
We have 24 such sets in 96 terms. So, 24* 5 + the 97th term which is 2

120+2=122. Thats what I think. So, I was wondering if I got the an expression wrong. Any thoughts?

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by mmukher » Sun Mar 23, 2008 1:10 pm
I got the same answer too. 122. Using the same logic...
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by camitava » Sun Mar 23, 2008 8:14 pm
Guys agree with Madhavi & mmukher! I think the Qs is having some issue with it or the answer choice ...
Correct me If I am wrong


Regards,

Amitava
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by HarvardDreamin » Sun Mar 23, 2008 11:26 pm
camitava wrote:Guys agree with Madhavi & mmukher! I think the Qs is having some issue with it or the answer choice ...
the answer is supposed to be 74. I got this question from the Sets group of question and thought that maybe I had made an error. I guess we should probably have one of the mods have a look - if they also concur with 122 then suggests the answer choices are wrong.
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by gabriel » Mon Mar 24, 2008 6:22 am
Well, me getting the answer as 122 to .. HD you sure it asks for the first 97 terms.
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by HarvardDreamin » Mon Mar 24, 2008 9:42 am
gabriel wrote:Well, me getting the answer as 122 to .. HD you sure it asks for the first 97 terms.
Yes. I think its an error with the question.
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