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 Question from Arjun, a student: 1/2 3/5 5/8 7/11- need to find the nth term. I did search the data base & found one for fractions but what I want to know is when calculating nth term for the denominator in the example give in your database how do we get (n-1)? When we deduct the actual term with the one that is in the table give in your example it is more that one. Could you please explain solving the above example? I thank you for your support. Arjun

Arjun,

I think you are looking at the question that Zarinah sent us. She sent the sequence

1/4, 2/7, 3/10, 4/13, 5/16, ...

In my response I let N designate numerator and D denominator and constructed the table.

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)

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.

1st term 2nd term 3rd term 4th term 5th
N 1 1 + 1(1) 1 +2(1) 1 + 3(1) 1 + 4(1)
D 4 4 + 1(3) 4 + 2(3) 4 + 3(3) 4 + 4(3)

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.

To obtain the second term you add 1 to the numerator and 3 to the denominator once.
To obtain the third term you add 1 to the numerator and 3 to the denominator twice.
To obtain the fourth term you add 1 to the numerator and 3 to the denominator three times.
To obtain the fifth term you add 1 to the numerator and 3 to the denominator four times.

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

To obtain the nth term you add 1 to the numerator and 3 to the denominator n-1 times.

Thus the nth term is [1 + (n-1)(1)]/[4 + (n-1)(3)].

I hope this helps,
Penny

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