Trigonometric EquationHard

Question

If the 2nd, 5th and 9th terms of a nonconstant A.P. are in G.P., then the common ratio of this G.P. is:

Options

A.

43

B.

1

C.

74

D.

85

Solution

Let the G.P. be a, ar, ar2 and terms of A.P. are A + d, A +4d, A + 8d
then ar2 - arar- a=(A+8d) -(A+4d)(A+4d)-(A+d)=43⇒r=43

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