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CAT-2007-Previous Years Paper

Question
6 out of 25
 

Let a1 = p and b1 = q, where p and are positive quantities.

Define an = pbn–1, bn = qbn–1, for even n > 1. and an = pan–1, bn = qan–1, for even n > 1.


Which or the following best describes an + bn for even n?



A

B

C

D

E

a1 = pb1 = q

n = 2 : a2 = p b1 = pq b2 = q b1 = q2

n = 3 : a3 = pq2 = p2q ; b3 = qa2 = pq2

n = 4 : a4 = pb3 = p2q2 ; b4 = qb3 = pq3

n = 5 : a5 = pa4 = p3q2 ; b5 = qa4 = p2q3

n = 6 : a6 = pb5 = p3q3 ; b6 = qb2 = p2q4

n = 7 : a7 = pa6 = p4q3 ; b7 = qa6 = p3q4


Ans. D

a2+ b2= pq + q2= q(p+q)

a4+ b4= p2q2+ pq3=pq2(p+q) =q(pq)(p+q)

a6+ b6= p3q3+ p2q4= p2q3(p+q) = q(pq)2(p+q)

Hence in general,

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