If sum of first n terms of an A.P. (having positive terms) is given by S n = (1 + 2T n ) (1 – T n ) where T n is the n th term of series, then T 22 = 
, (a ∈ N, b ∈ N), then find the value of (a + b)
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Sol. S n = (1 + 2T n )(1 – T n ) ⇒ T 1 = (1 + 2T 1 ) (1 – T 1 )
T 1 = 1 – T 1 + 2T 1 – 2T 12 ⇒ 2T 12 = 1 ⇒ T 1 = 
S 2 = T 1 + T 2 = (1 + 2T 2 ) (1 – T 2 ) ⇒ T 1 + T 2 = 1 – T 2 + 2T 2 – 2T 22
T 1 = 1 – 2 T 22 ⇒ 2T 22 = 1 – 
T 22 = 
⇒ T 22 = 
⇒ a = 4, b = 2 ⇒ a + b = 6
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