Insert three fractions between 1/4 and 1/ so that all five of the fractions form an arithmetic sequence?

Question

and please show how you did it

Answer 1

The difference between 1 and 1/4 is:
1 - 1/4 = 3/4

You are going to stick in 3 evenly spaced fractions, which means you need to divide by *4*. (Think about this for a second, the fractions act like "dividers" so 3 dividers break the interval into *4* sections...)

Okay, back to the question:
3/4 divided by 4:

3/4 * 1/4 = 3/16

So each interval from one fraction to the next is 3/16. Starting with 1/4, add 3/16.

1/4 + 3/16
= 4/16 + 3/16 = 7/16

Continue with adding another 3/16:
7/16 + 3/16 = 10/16
= 5/8

Continue adding another:
10/16 + 3/16 = 13/16

And another:
13/16 + 3/16 = 16/16
= 1

You did it! The sequence is:
1/4, 7/16, 5/8, 13/16, 1