1 = 2/2
2/9 = 4/18

Put them together,

2/2 , 3/8 , 4/18 , 5/32

Notice that for the numerators :

Term number + 1 = numerator


For the denominators:

First term = 2 = 1 x 2 = 1 x 1 x 2 = 3² x 2
Second term = 8 = 2 x 4 = 2 x 2 x 2 = 2² x 2
Third term = 18 = 3 x 6 = 3 x 3 x 2 = 3² x 2
Fourth term = 32 = 4 x 8 = 4 x 4 x 2 = 4² x 2


It is always a product of 2 and the square of the term number.


So for the nth term,

Numerator = n + 1
Denominator = 2n²

nth term is (n+1)/2n²

This is the Answer for part (ii)

Next two terms of the sequence :


6/(2x5²) = 6/50 = 3/25

7/(2x6²) = 7/72

99th term :


100/(2x99²)

= 100/19602

= 50/9801