5, x, 13, y , .... is an A.P

Then,

a1= 5

a2= 5 + r = x

a3= 5 + 2r = 13

==> 2r = 13-5 = 8

==> r = 8/2 = 4

==> a2= 5 + r = x

==> 5 + 4 = x

==> **x =9**

==> y = 13 + r

= 13 + 4 = 17

**==> y= 17**

For this sequence, the answer is that x is 9 and y is 17. The difference between each set of terms in this sequence is 4.

We can find this by the fact that the difference between 5 and 13 is 8. We know that, in an arithmetic sequence, the difference between each pair of numbers is constant. Therefore, the difference between 5 and 13 must be split equally into the intervals between 5 and x and x and 13. 8 divided by 2 is 4 and therefore the difference between each pair of terms is 4.

Once we know that the difference between each pair of terms is 4, we simply add 4 to 13 to get the value for y.