Question

If 18, x,y-3are in A.P the value of x+y.​

Answer 1

Correct Question :

If 18, x, y, -3 are in AP . Then find the value of x+y

Solution :

Given AP : 18 , x , y, -3

Common difference

d =x -18= y-x = -3-y

Thus , x -18 = y - x

⇒2x - y = 18 ..(1)

and -3-y = y - x

⇒x-2y = 3

⇒x = 3+2y ...(2)

Now ,Put the value x = 3+2y in equation (1)

Then, 2( 3+2y )-y = 18

⇒6+4y -y = 18

⇒ 3y = 18-6

⇒3y = 12

⇒ y = 4

Put y = 4 ,in equation (2)

Then , x= 3+2(4)

⇒ x = 8+3 = 11

Therefore, the value of

x+ y = 11+4 = 15

$\rule{200}2$

More About Arithmetic Progression:

•Genral term of an Ap

$\sf a_{n} = a + (n - 1)d$

•Sum of first n terms of an AP

$\sf \: s_{n} = \dfrac{n}{2} (2a + (n - 1)d)$