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If the variance of the terms in an increasing A . P . b 1 b 2 , b 3 , … … . . , b 11 is 90 then the common difference of this A . P . is

Correct answer

3

Step-by-step solution

Given b 1 , b 2 , b 3 , … . . b 11 , are in A . P . ∴ Variance of b 1 , b 2 , … . . b 11 = Variance of ( 0 , d , 2 d , … . . 10 d ) = 90 ⇒    ∑ i = 1 11 b i 2 11 - ∑ i = 1 11 b i 11 2 = 90 ⇒    d 2 11 · 10 . 11 . 21 6 - d 2 · 55 11 · 55 11 = 90 ⇒    35 d 2 - 25 d 2 = 90 ⇒    d 2 = 9   ⇒ d = ± 3 It is an increasing A . P .   ⇒ d is positive. ⇒    d = 3

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