Solve for x : 1 + 4 + 7 + 10 + ... + x = 287.

The above series is in A.P. because, any term - preceding term = 3 = common difference. Let there be n terms so, x = a n . Given, a = 1, d = 3 and S n = 287. By formula, S n = Since number of terms cannot be negative so n ≠ ∴ n = 14. We know x = a n so, ⇒ x = a + (n - 1)d ⇒ x = 1 + (14 - 1)3 ⇒ x = 1 + 13(3) ⇒ x = 1 + 39 ⇒ x = 40. Hence, the value of x = 40.