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.”

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.

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.

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).