How Do You Find the Nth Term of Fractions?
To find the nth term of a fraction, find the pattern in the first few terms of the sequence for the numerator and denominator. Then write a general expression for the sequence of fractions in terms of the variable “n.”
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Find the pattern in the numerator
First find the pattern in the numerators of the fraction sequence. It is helpful to make a chart. For example, in the fraction sequence 2/3, 3/5, 4/7, 5/9, the numerator starts with 2 and then increases by 1 each time.
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Find the pattern in the denominator
Use the same process to find the pattern for the denominator. To continue the example, the denominators start with 3 and increase by 2 each time.
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Write the general expression
Write a general expression for the fraction sequence that shows the pattern, using “n” as the variable. The example numerator sequence is n +1. The denominator sequence is 2n + 1. Thus, the entire general expression is (n + 1) / (2n + 1).
