Question

The sum of 5 and 15 terms of an A.P. are equal. Find the sum of 20 terms of this A.P.

Answer 1

We are given that the sum of 5 terms (S₅) is equal to the sum of 15 terms (S₁₅)

(S₅) = (S₁₅)

`5/2[2a + (4)d] = 15/2[2a + 14(d)]`

2a + 4d = 6a + 42d

−4a = 38d

a = `(-38d)/4`

a = `(-19d)/2`

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

`S_20 = 20/2[2((-19d)/2) + (20 - 1)d]`

`S_20 = 10[2((-19d)/2) + 19d]`

S₂₀ = 10[-19d + 19d]

S₂₀ = 10 × 0

S₂₀ = 0