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Sequences

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by shankar.ashwin » Tue Nov 08, 2011 3:56 am
A sequence of numbers is represented as s1, s2, s3, ..., sn. Each number in the sequence (except the first and the last) is the mean of the two adjacent numbers in the sequence. If s1 = 1 and s5 = 3, what is the value of s3 ?

A) 1/2
B) 1
C) 3/2
D) 2
E) 5/2
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by rijul007 » Tue Nov 08, 2011 4:02 am
s1 = 1
s5 = 3
s3 = x

s1 s2 s3 s4 s5


s2 = (1+x)/2
s4 = (3+x)/2

s3 = (s2+s4)/2
x = [(4+2x)/2]/2
2x = 2 + x
x = 2

s3 = 2

Option D
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by user123321 » Tue Nov 08, 2011 4:02 am
in AP, any term will be always mean of its adjacent terms except first and last.

hence s1 = 1 =a
s5 = a+4d = 3
=> d = 0.5 and a = 1
s3 = a+2d = 1+0.5*2 = 2

IMO D

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by Anurag@Gurome » Tue Nov 08, 2011 4:03 am
shankar.ashwin wrote:A sequence of numbers is represented as s1, s2, s3, ..., sn. Each number in the sequence (except the first and the last) is the mean of the two adjacent numbers in the sequence. If s1 = 1 and s5 = 3, what is the value of s3 ?
s4 = (s3 + s5)/2 = (1 + s3)/2
s2 = (s1 + s3)/2 = (3 + s3)/2

--> s3 = (s2 + s4)/2 = [(1 + s3)/2 + (3 + s5)/2)]/2 = [2 + s3]/2
--> s3 = 2

The correct answer is D.
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by GMATGuruNY » Tue Nov 08, 2011 4:36 am
shankar.ashwin wrote:A sequence of numbers is represented as s1, s2, s3, ..., sn. Each number in the sequence (except the first and the last) is the mean of the two adjacent numbers in the sequence. If s1 = 1 and s5 = 3, what is the value of s3 ?

A) 1/2
B) 1
C) 3/2
D) 2
E) 5/2
Almost no math is needed here.

Every term is the average of the two terms surrounding it. In other words, every term is HALFWAY between the two terms surrounding it.
This means that all of the terms in the sequence are EVENLY SPACED.
Thus, the 3rd term must be HALFWAY between the 1st term (1) and the 5th term (3).

The correct answer is D.
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