Zarinah,
I used a table to try to see what the pattern is. In the table below N is the numerator and D is the denominator.

1st term 
2nd term 
3rd term 
4th term 
5th 
N 
1 
1 + 1 
1 +2(1) 
1 + 3(1) 
1 + 4(1) 
D 
4 
4 + 3 
4 + 2(3) 
4 + 3(3) 
4 + 4(3) 
In the first term N = 1 and D = 3. In the second term you add 1 to N and 3 to D. (I wrote the numbers you add in red so that they would stand out.) In the third term you add another 1 to N and another 3 to D. Thus in the third term you have 1 plus 2 ones in the numerator and 4 plus 2 threes in the denominator. Likewise in the fourth term you have 1 plus 3 ones in the numerator and 4 plus 3 threes in the denominator.
I hope now you see the pattern. In every term the numerator is 1 + k(1) and the denominator is 4 + k(3) for some number k. The number k is one less than the term number, that is for the third term k = 2, for the fourth term k = 3, etc.
Now I can see the nth term, the numerator is 1 + (n1)(1) and the denominator is 4 + (n1)(3).
Write this fraction, simplify it and then check that when n = 1, 2, 3, ... you get the correct answers.
Penny
