Q2Short answer
p−q . Solution Let A be the first term and D be the common difference of the A.P. It is given that tp = a ⇒ A + (p – 1) D = a ... (1) tq = b ⇒ A + (q – 1) D = b ... (2) Subtracting (2) from (1), we get (p – 1 – q + 1) D = a – b a−b ⇒ D= p−q ... (3) Adding (1) and (2), we get 2A + (p + q – 2) D = a + b ⇒ 2A + (p + q – 1) D = a + b + D a−b ⇒ 2A + (p + q – 1) D = a + b + p − q .. (4) p+q Now Sp + q = [2A + (p + q – 1) D] p+q a−b = a+b+ 2 p−q [(using ... (3) and (4)]