Discussion

Explanation:

a, b, c form an AP.
∴ 2b = a + c 
Increasing a by 1 or c by 2 results in a GP

∴ b2 = (a + 1)c      …(1)
and b2 = a(c + 2)   …(2)

∴ (a + 1)c = a(c + 2)
∴ ac + c = ac + 2a
∴ c = 2a

Now, 2b = a + c
∴ 2b = a + 2a
∴ b = 3a/2

Putting this in (1), we get
(9a2)/4 = (a + 1)2a
∴ 9a/4 = 2a + 2
∴ 9a = 8a + 8
∴ a = 8

∴ b = 3a/2 = (3×8)/2 = 12

Hence, option (c).

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