Solve for x

1 + 6+11 + 16 +...+x= 148

Here, a = 1, d = 6 – 1 = 5 and S_n = 148

⇒ 296 = n[5n – 3]

⇒ 5n² – 3n – 296 = 0

⇒ 5n² – 40n + 37n – 296 = 0

⇒ 5n(n – 8) + 37(n – 8) = 0

⇒ (5n + 37)(n – 8) = 0

⇒ 5n + 37 = 0 or n – 8 = 0

⇒ or n = 8

But is not a positive integer.

∴ n = 8

⇒ x = a₈ = a + 7d = 1 + 7 × 5 = 1 + 35 = 36

Hence, x = 36