Question
If a, 1, b are in arithmetic progression and 1, a, b are
in geometric progression, then a and b are respectively equate to _______ (where a ≠ b).Solution
Given a, 1, and b are in AP and 1, a, and b are in GP: From AP= 1- a=b-1 b=2- a … (1) From GP- b = a² … (2) from Eq (1) and Eq (2) a² = 2-a a²+a-2=0 a2+2a- a -2 =0 a = 1 or - 2 Since a ≠ 1: a = -2 b = a² = 4 So, a = -2 and b = 4. Alternate method- According to the option- (a + b)/2 = 1 (a + b) = 2 Put the value of a and b in the option and satisfied. Taking option 2. (-2 + 4) = 2 2 = 2 (satisfied)
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