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some expert reply pls!!!

by finance » Thu Jul 21, 2011 2:05 am
A sequence of numbers (geometric sequence) is given by the expression: gn=5*(-1/2)^n . If the sequence begins with n = 1, what are the first two terms for which |gn-g(n+1)|<(1/1000)?

a) g10,g11
b) g11,g12
c) g12,g13
d) g13,g14
e) g14,g15

Do they ask such questions full of calculations on GMAT?

Thanks in advance!
Last edited by finance on Thu Jul 21, 2011 2:47 am, edited 2 times in total.
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by amit2k9 » Thu Jul 21, 2011 2:24 am
well I am not sure the question is complete or not.
However taking, |gn -(gn+1)| < 1/1000 as the question.

g1 = -5/2 g2= 5/4, g3= -5/8, g4= 5/16

hence g12= 5/2^12 = 5/4096
g13 = -5/2^13 = -5/8192 and g14 = 5/2^14 = 5/16384

thus for |gn -(gn+1)| = |-5/2^13 + 5/2^14 | = 15/2^14 < 1/1000 (you can check by cross multiplication)

thus, D it is.
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