Question

Write the first five terms of the sequences whose n^th term is:

`a_n = n (n^2 + 5)/4`

Answer 1

a_n = `"n"("n"^2 + 5)/4` 

Substituting n = 1, 2, 3, 4, 5, we get

a₁ = `1 (1^2 + 5)/4 = 6/4 = 3/2`,

a₂ = `2 (2^2 + 5)/4 = (2 xx 9)/4 = 9/2`,

a₃ = `3 (3^2 + 5)/4 = (3 xx 14)/4 = 21/2`,

a₄ = `4 (4^2 + 5)/4 = (4 xx 21)/4` = 21,

a₅ = `5 (5^2 + 5)/4 = (5 xx 30)/4 = 75/2`

Hence, the five terms of the sequence are `3/2, 9/2, 21/2, 21, 75/2`.