If3,x,y,18 are in arithmetric progression , find the value of x and y
x-3 = 18-y
x-3 = y -x
so
x+y = 21
-2x + y = -3
------------
3 x = 24
x = 8
then y = 21-8 = 13
so
3 , 8 , 13 , 18
difference is always 5
Convert 42 base 5 to a base 3 numeral
Thanks very much
To find the values of x and y in the arithmetic progression given as If3, x, y, 18, we need to first understand what an arithmetic progression (AP) is.
In an AP, the difference between any two consecutive terms is constant. Let's call this common difference "d".
Here, the given terms are If3, x, y, 18.
The difference between the first term (If3) and the second term (x) is equal to the difference between the second term (x) and the third term (y). We can set up an equation using this information.
The equation for an AP is: (n-th term) = (first term) + (n-1) * (common difference)
Using this equation, we can write:
x = If3 + (2) * d ...(1)
y = x + d ...(2)
18 = y + d ...(3)
Now we have a system of three equations with three unknowns (x, y, d).
To solve this system, we'll use the method of substitution.
Substitute equation (1) into equation (2):
y = (If3 + 2d) + d = If3 + 3d
Substitute equation (2) into equation (3):
18 = (If3 + 3d) + d = If3 + 4d
Rearrange equation (3) to solve for If3:
If3 = 18 - 4d ...(4)
Substitute equation (4) back into equation (1):
x = If3 + (2) * d
x = (18 - 4d) + 2d
x = 18 - 2d ...(5)
Now we have two equations with two unknowns (x, d).
Substitute equation (5) into equation (2):
y = x + d
y = (18 - 2d) + d
y = 18 - d ...(6)
We can now substitute equation (4) into equation (6) to solve for d:
18 - d = 18 - 4d
Simplifying the equation, we get:
3d = 0
Dividing both sides by 3, we find:
d = 0
Now that we know the common difference (d = 0), we can substitute it back into equation (5) to find the value of x:
x = 18 - 2d
x = 18 - 2(0)
x = 18
Similarly, substitute d = 0 into equation (6) to find the value of y:
y = 18 - d
y = 18 - 0
Therefore, the value of y is also 18.
Hence, the values of x and y in the arithmetic progression If3, x, y, 18 are x = 18 and y = 18.