Terms a, 1, b are in Arithmetic Progression and terms 1,

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Terms a, 1, b are in Arithmetic Progression and terms 1, a,b are in Geometric Progression. Find ‘a’ and ‘b’ given a ≠ b.

1. 2,4
2. –2, 1
3. 4,1
4. –2, 4

Correct Option: D

As per the given question ,
a, 1, b are in A.P.

∴ Mean =	a + b
	2

∴ 1 =	a + b
	2

⇒ a + b = 2 ....(i)
Again, 1, a, b are in G.P.
∴ a² = b ......(ii)
∴ a + a² = 2
⇒ a² + a – 2 = 0
⇒ a² + 2a – a – 2 = 0
⇒ a (a + 2) – 1 (a + 2) = 0
⇒ (a – 1) (a + 2) = 0
⇒ a = –2 , 1 and b = 4 , 1
∴ b = 4 since a ≠ b