Question

if the sum of the sum of the first and n term of an ap is 4 n -n square then find it is a common difference

Answer 1

Hi !

Sn = 4n - n²

S₁ = 4(1) - 1² =  3
S₂ = 4(2) - 2² = 4
S₃ = 4(3) - 3² = 3
S₄ = 4(4) - 4² = 0

First term = a₁ = S₁ = 3
Second term = a₂ = S₂ - S₁ = 4 - 3 = 1
Third term = a₃ = S₃ - S₂ = 3 - 4 = -1

Common difference = a₂ - a₁ = 1 - 3 = -2