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Q.

Let  α and β be the roots of the equation x2−x−1=0. If Pk=αk+βk, for each  k∈N, then which one of the following statements is not true? 

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a

P5=P2.P3

b

P3=P5−P4

c

P5=11

d

P1+P2+P3+P4+P5=26

answer is D.

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Detailed Solution

P1=α+β=1, P2=α2+β2=12−2(−1)=3

Pk+2−Pk+1−Pk=0

∴ P3=P1+P2=4,   P4=P2+P3=7

P5=P3+P4=11

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