Question

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

`a_n = (2n -3)/6`

Answer 1

a_n = `(2"n" - 3)/6` 

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

a₁ = `(2 xx 1 - 3)/6 = (2 - 3)/6 = -1/6`,

a₂ = `(2 xx 2 - 3)/6 = (4 - 3)/6 = 1/6`,

a₃ = `(2 xx 3 - 3)/6 = (6 -3)/6 = 3/6 = 1/2`

a₄ = `(2 xx 4 - 3)/6 = (8 - 3)/6 = 5/6`,

a₅ = `(2 xx 5 - 3)/6 = (10 - 3)/6 = 7/6`

Hence, the five terms of the sequence are `-1/6, 1/6, 1/2, 5/6, 7/6`.