Question

What is the next fraction in each of the following patterns?1/40,4/40,9/40,16/40,25/40...?

Answer 1

Let
a1=1/40
a2=4/40
a3=9/40
a4=16/40
a5=25/40
a6=?

we know that
a2-a1=4/40-1/40----> 3/40
a3-a2=9/40-4/40-----> 5/40
a4-a3=16/40-9/40----> 7/40
a5-a4=25/40-16/40---> 9/40

the difference is
3/40,5/40,7/40.9/40,....
3/40+[2/40]---> 5/40
5/40+[2/40]---> 7/40
7/40+[2/40]---> 9/40

the next will be
9/40+[2/40]-----> 11/40
so
the next term is 25/40+[11/40]------> 36/40

the answer is
36/40