What is the next fraction in each following patterens 1/40, 4/40, 9/40, 16/40, 25/40

The numerator (top number of the fraction) is adding up by odd numbers in order.

From 1/40 to 4/40 you add 3, from 4/40 to 9/40 you add 5, from 9/40 to 16/40 you add 7, and from 16/40 to 25/40 you add 9.

The next number to add would logically be 11. So from 25/40 you would go to 36/40.

36/40 is your next fraction.