Consider an A.P.: a₁, a₂, , a_ n ; a₁>0 . If a₂-a₁= -3 4 , a_ n = 1 4 a₁ , and _ i =1 ^ n a_ i = 525 2 , then _ i =1 ¹⁷ a_ i is equal to

Step-by-step solution

Common difference d = a₂ - a₁ = -3/4 . a_n = a₁ + (n-1)(-3/4) = a₁/4 3a₁/4 = 3(n-1)/4 a₁ = n-1 . S_n = n 2 (a₁ + a_n) = n 2 5a₁ 4 = 5na₁ 8 = 525 2 na₁ = 420 . Since a₁ = n-1 : n(n-1) = 420 n = 21, ; a₁ = 20 . _ i=1 ¹⁷ a_i = 17 2 (2 20 + 16 (-3/4)) = 17 2 (40 - 12) = 17 14 = 238