We have, an = n

n2+5

4

Substituting n = 1, 2, 3, 4, 5, we get
a1 = 1.

12+5

4

=

6

4

=

3

2

, a2 = 2.

22+5

4

=

2.9

4

=

9

2

a3 = 3.

35+5

4

=

3.14

4

=

21

2

, a4 = 4.

42+5

4

=

4.21

4

= 21
a5 = 5.

55+5

4

=

5.30

4

=

75

2

∴ The first five terms are

3

2

,

9

2

,

21

2

,21,

75

2