Question

In an A.P., if T₁ + T₅ + T₁₀ + T₁₅ + T₂₀ + T₂₄ = 225, find the sum of its 24 terms.

Answer 1

T₁ + T₅ + T₁₀ + T₁₅ + T₂₀ + T₂₄ = 225

(T₁ + T₂₄) + (T₅ + T₂₀) + (T₁₀ + T₁₅) = 225

(T₁ + T₂₄) = (T₅ + T₂₀) = (T₁₀ + T₁₅)

= 3(T₁ + T₂₄) = 225

T₁ + T₂₄ = `225/3`

`S_n = n/2(a + l)`

`S_24 = 24/2(T_1 + T_24)`

`S_24 = 24/2 xx 225/3`

S₂₄ = 12 × 75

S₂₄ = 900