If x , x + 1 and x - 1 are the first three terms of an arithmetic progression, then its sum upto 20 terms is

Step-by-step solution

2 x + 1 = x + x - 1 (i) Case- Ι :- x ≤ - 1 2 - x - 1 = x + - x + 1 ⇒ - 2 x - 2 = 1 ⇒ x = - 3 2 Then the A.P. is → - 3 2 , 1 2 , 5 2 . . . . . . S 20 = 20 2 - 3 + 19 × 2 = 20 2 × 35 = 35 0 (ii) Case- Ι Ι :- - 1 ≤ x < 1 2 x + 1 = x + - x + 1 ⇒ 2 x + 2 = 1 ⇒ x = - 1 2 Then the A.P. is → - 1 2 , 1 2 , 3 2 . . . . . . S 20 = 20 2 - 1 + 19 × 1 = 10 × 18 = 18 0 (ii) Case- Ι Ι Ι :- x ≥ 1 2 x + 1 = x + x - 1 ⇒ 2 x + 2 = 2 x - 1 ⇒ 2 = - 1 (not possible) Hence, the required sum is 350 or 180