Question

(i) S_n = n²(n + 1)

Answer 1

(i) Sum of n terms of a sequence, S_n = n²(n + 1)
To find the first three terms of the sequence, we need to find S₁, S₂ and S₃.

For n = 1, we have:
S₁ = 1²(1 + 1) = 1 × 2 = 2
For n = 2, we have:
S₂ = 2²(2 + 1) = 4 × 3 = 12
For n = 3, we have:
S₃ = 3²(3 + 1) = 9 × 4 = 36

Thus, we get:
t₁ = S₁ = 2
t₂ = S₂ – S₁ = 12 – 2 = 10
t₃ = S₃ – S₂ = 36 – 12 = 24

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