Write the first 6 terms of the sequence with an nth term of

Write the first 6 terms of the sequence with an nth term of a_n = (2 + n)/n^2.

Solution

We need to find first six terms of the sequence

a_n = (2+n)/n²

to find the first term we put n = 1 in the equation of a_n.

a₁ = (2+1)/1²

a₁ = 3/1

a₁ = 3

to find the second term of the sequence we subtituite n=2 in the equation for a_n

a₂ = (2+2)/2²

a₂ = 4/4

a₂ = 1

to find the third term of the sequence we put n=3

a₃ = (2+3)/3²

a₃ = 5/9

to find the fourth term of the sequence we put n=4

a₄ = (2+4)/4²

a₄ = 6/16      or 3/8

a₄ = 3/8

to find the fifth term of the sequence we put n=5

a₅ = (2+5)/5²

a₅ = 7/25

to find the sixth term of the sequence we put n=6

a₆ = (2+6)/6²

a₆ = 8/36 or 4/18 or 2/9

a₆ = 2/9