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Question

Out of four number in a sequence,first three are in GP with first term 2 and last three are in AP with common difference 12. Find the common ratio, if the number are positive.


A

2

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B

3

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C

4

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D

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Solution

The correct option is B

3


t1 = 2r

t2 = 2r

t3 = 2r2

There are the first three terms which are in GP last three terms in AP are

T2 = 2

T3 = 2r + 12

T4 = 2r + 24

Equating t3 in AP and GP

2r + 12 = 2r2

r2 - r - 6 = 0

(r - 3) (r + 2) = 0 r = 3 [r is +ive]


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