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infinite sequence

by GmatKiss » Sat Aug 13, 2011 1:54 pm
The infinite sequence a1, a2,�, an,� is such that a1 = 3, a2 = -1, a3 = 6, a4 = -2, and an = an-4 for n > 4. What is the sum of the first 83 terms of the sequence?

A. 120
B. 124
C. 128
D. 132
E. 136
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by sumgb » Sun Aug 14, 2011 6:42 am
Important thing here is to recognize the pattern,

a1 = 3
a2 = -1
a3 = 6
a4 = -2

an = an-4 which means,
a5 = a1
a6 = a2
a7 = a3
a8 = a4 and again
a9 = a5 = a1
a10 = a6 = a2 and so on...

so the values repeat after interval of 4;

3,-1,6,-2,3,-1,6,-2,..... etc

addition of first 4 terms = 3 + -1 + 6 + -2 = 6
addition of next 4 terms = addition of first 4 terms = 6
let's call this as addition of "1 group", so in first 80 terms we have 20 such groups
so addition of first 80 terms = 6 * 20 = 120
81st term = 3; 82nd term = -1 and 83rd term = 6
so addition of first 83 terms = 120 + 3 + -1 + 6 = 128

hence the answer C.

Hope this helps.
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by GmatKiss » Sun Aug 14, 2011 11:30 am
Is it, an = a(n-4)! i thought it to be (an)-4 :(

thanks a ton sungb :)
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