Question

If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference of this A.P. is : 

(1) 1 / 4 

(2) 1 / 5 

(3) 1 / 7 

(4) 1 / 6

Answer 1

(4) 1 / 6 

Sum of 1st 25 terms = sum of its next 15 terms 

⇒ (T₁ + ..... + T₂₅) = (T₂₆ + ..... + T₄₀ ) 

⇒ (T₁ + ..... + T₄₀) = 2(T₁ + ...... + T₂₅ ) 

⇒ 40 / 2 [2 × 3 + (39d)] = 2 × 25 / 2 [2 × 2 + 24d] 

⇒  d = 1 / 6