Question

In an A.P. the first term is 2, and the sum of the first five terms is one-fourth of the next five terms. Show that its 20th term is -112.

Answer 1

Given: first term, a = 2

And

⇒ 20 + 20d = 8 + 18d

⇒ 20d – 18d = 8 – 20

⇒ 2d = -12

⇒ d = -6

Thus, a = 2 and d = -6

∴ a₂₀ = a + (n – 1)d

⇒ a₂₀ = 2 + (20 – 1)(-6)

⇒ a₂₀ = 2 + (19)(-6)

⇒ a₂₀ = 2 – 114

⇒ a₂₀ = -112

Hence Proved