If 8,x,y,z and 20 are in A.P.find x,y,z

y-x = x-8

y = 2x-8

z-y = y-x
z = 2y - x
= 2(2x-8) - x = 3x - 16

20-z = z-y
y = 2z - 20
2x - 8 = 2(3x-16)-20
2x-8 = 6x - 32-20

4x = 44
x = 11
y = 22-8 = 14
z = 33-16 = 17

or, simplest way:

4d = 20-8
d = 3

so the terms are 8, 11, 14, 17, and 20
match the x,y, and z

if 8,x,y,2 and 20 are in A.p find x and y?

If 8,x,y,z and 20 are in AP.Find x,y,and z

To find the values of x, y, and z in the arithmetic progression (A.P.) with 8, x, y, z, and 20, we need to use the formula for the nth term of an A.P.

In an A.P., the difference between any two consecutive terms is constant. Let's call this common difference "d."

We can find the common difference, d, by subtracting the first term from the second term:

d = x - 8

Now, to find x, y, and z, we need to find the values of d+d, d+2d, and d+3d.

The second term, x, is equal to 8 + d.
The third term, y, is equal to 8 + 2d.
The fourth term, z, is equal to 8 + 3d.

Since we know that the fifth term, 20, is in the A.P., we can set up an equation using the fourth term:

20 = 8 + 3d

Now, we can solve this equation for d:

20 - 8 = 3d
12 = 3d
d = 4

Now that we have the value of d, we can find the values of x, y, and z:

x = 8 + d
y = 8 + 2d
z = 8 + 3d

Substituting the value of d, we get:

x = 8 + 4 = 12
y = 8 + 2(4) = 16
z = 8 + 3(4) = 20

Therefore, the values of x, y, and z in the A.P. are 12, 16, and 20, respectively.