Find the value of x and y in the arithmetic sequence ( 5,x,13,y....)

The  first 4 terms of the given arothmetoc progression are
5,x,a3 and y.

To find x and
y..

Solution:

In an arithmetic
progression, the rth term ar  is given by:

ar = a1+(r-1)d,
where d is the common difference.

So a1 =
5.

a3 = a1+(3-1)d = a1+2d.,

2d
= a3-a1 = 13-5 = 8

d = 8/2
=4.

Therefore the common diffrence =
4.

So a2 = x = a1+(2-1)d = 5+1*4 =
9

a4 = y = a1+(4-1)d = 5+3*4 = 
17.

So  x= 9 and y =
17.

Tally.

So the the 1st 4
terms of AP = 5, 9, 13 and 17