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Two distinct, real, infinite GP each have a sum to infinite no of terms=1 and have common second term and of the series have 1/8 as their third term. If the second term of both the GPs can be written in the form (√m - n)/p where m,n and p are positive integers and m is not divisible by the square of any prime, find the value of 100m+10n+p.
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4 Answers
1357a/(1-r)=1, a1r1=a2r2
from first and second (r1-r2)(r1+r2-1)=0
implies r1+r2=1
a1r12=1/8
(1-r)r2=1/8
solving it we get r=1/2,(1±√5)/4
r cannot be 1/2
so ar=(1-r)r=(1-(1±√5)/4)(1±√5)/4=(1/16)(3-(±√5))(1±√5)
=(1/16)(3±2√5-5)=(1/16)(2√5-2)=(1/8)(√5-1)
m=5, n=1 and p=8
6Yes the mentor is absolutely right! the correct answer is 518