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.?

2, a, b are in GP and 2,17, a are in
AP.

Consider the AP : 2,17, a. So the common difference d
is 2nd term - 1st term = d = 17-2 = 15.

Therefore d =
15.

So the 3rd term a = 2nd term +d = 17+15 =
32.

So now Put a = 32 in the GP is 2,  a,  b. So the given
GP is 2, 3, b.

=> the common ratio r of the GP is =
2nd term / first term = 32/2 = 16.

So the 3rd term of the
GP is b = 2nd term * r = 32* 16 = 512.

Therefore a = 32 and
b = 512.