If the first, second and last term of an A.P. are a, b and 2a respectively, its sum is

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In the given problem, we are given first, second and last term of an A.P. We need to find its sum. So, here First term = a Second term (a2) = b Last term (l) = 2a Now, using the formula an = a+ ( n - 1) d a2 = a + (2 - 1)d b = a + d d = b - a ......(1) Also, an = a + (n-1) d 2a = a + nd - d 2a - a = nd - d (a + d)/d = n ...........(2) Further as we know, S_n = n/2 [ a + l] Substituting (2) in the above equation, we get Using (1), we get `S_n = ( a + (b - a) )/(2(b - a)) (3a) S_n =b / ( 2 ( b-a) ) (3a) Thus, S_n = (3ab)/(2(b-a))`

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