Solve the equation 2 + 5 + 8 + .... + x = 155.

The above series is an A.P. with a = 2, d = 5 - 2 = 3 and Sum = 155. Let x be nth term so, a n = a + (n - 1)d. ⇒ x = 2 + (n - 1)3 ⇒ x = 2 + 3n - 3 ⇒ x = 3n - 1. Sum = Since, number of terms cannot be in fraction so, ≠ ∴ x = 3n - 1 = 3 × 10 - 1 = 30 - 1 = 29. Hence, the value of x is 29.