Question

Solve the equation: 1 + 4 + 7 + 10 + ... + x = 287.

Answer 1

Given, a = 1 and d = 4 – 1 = 3

Let number of terms is the series be n, then

`S_n = n/2 [2a + (n - 1)d]`

⇒ `n/2 [2 xx 1 + (n - 1)3] = 287`

⇒  `n/2 [2 + 3n - 3] = 287`

⇒ 3n² – n – 574 = 0

⇒ 3n² – 42n + 41n – 574 = 0

⇒ 3n (n – 14) + 41 (n – 14) = 0

⇒ (n – 14) (3n + 41) = 0

Either n = 14 or n = `- 41/3`, it is not possible

Thus 14^th thus is x

∴ a + (n – 1) d = x

⇒ x = 1 + 13 × 3

⇒ x = 40