What are a,b, if 2,a,b are the terms of a g.p. and 2,17,a are the terms of an a.p.?

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We are given that 2, a, b are the terms of a geometric progression and 2, 17 , a are the terms of an arithmetic progression.

Now for an A.P. , if we consider three terms, the sum of the first and third terms is twice the second term.

=> 2 + a = 2*17

=> 2 + a = 34

=> a = 32

Now the terms of the G.P. are 2, 32, b

=> (32 / 2) = (b / 32)

=> 16 = b / 32

=> b = 32* 16

=> b = 512

Therefore a  = 32 and b = 512.

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