Question

if 5, x, y, 26 are in AP then find X and Y

Answer 1

Given,
5, x, y, 26 are in A.P.

∴ x - 5 = y - x = 26 - y

Now,
x-5 = y-x

or 2x - y = 5 ..........(1)

And,
y-x = 26-y

or 2y -x = 26 ..............(2)

(1) × 2 + (2), we get

4x -2y + 2y - x = 10 + 26

or 3x = 36

or x = 12

Now, (1)⇒ 2x - y = 5

⇒2×12 -y = 5

⇒ 24 -y = 5

⇒y = 19

Thus, x = 12 and y = 19