Question

Solve for x

25 + 22 + 19 + 16 +... + x = 115

Answer 1

Here, a = 25, d = 22 – 25 = -3 and S_n = 115

⇒ 230 = n[53 – 3n]

⇒ 3n² – 53n + 230 = 0

⇒ 3n² – 30n - 23n + 230 = 0

⇒ 3n(n – 10) - 23(n – 10) = 0

⇒ (3n – 23)(n – 10) = 0

⇒ 3n – 23 = 0 or n – 10 = 0

⇒ n = 23/3 or n = 10

But n = 23/3 is not an integer.

∴ n = 10

⇒ x = a₁₀ = a + 9d = 25 + 9 × (-3) = 25 – 27 = -2

Hence, x = -2