Sn = n2(n + 1)

(i) S_n = n²(n + 1) (2 marks)

Sol. S_n = n²(n + 1)

∴ S₁ = 1² (1 + 1) = 1 (2) = 2

∴ S₂ = 2² (2 + 1) = 4 (3) = 12

∴ S₃ = 3² (3 + 1) = 9 (4) = 36

We know that,

t₁ = S₁ = 2

t₂ = S₂ – S₁ = 12 – 2 = 10

t₃ = S₃ – S₂ = 36 – 12 = 24

∴ The first three terms of the sequence are 2, 10 and 24.