



 
Arjun, I think you are looking at the question that Zarinah sent us. She sent the sequence
In my response I let N designate numerator and D denominator and constructed the table.
I you look at the terms in the sequence you will see that the numerators are increasing by 1 (1, 2, 3, 4, ...) and the denominators are increasing by 3 (4, 7, 10, 13, ...). I highlighted this in the table by using the colour red. I am going to draw the table again and this time highlight a different number in blue.
So the sequence starts at 1/4 and then to obtain subsequent terms you add ones to the numerator and threes to the numerator. The blue numbers tell you how many times you have added 1 to the numerator and 3 to the denominator.
So the number of times you add 1 to the numerator and 3 to the dominator is one less than the term number. That is
Thus the nth term is [1 + (n1)(1)]/[4 + (n1)(3)]. I hope this helps,  


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