The consecutive terms of an arithmetic progression are 5-x, 8, 2x. Find the common difference of the progression.
The common difference of an A.P. is constant, therefore, we can take the difference of consecutive terms and equate the values to determine x:
2x-8 = 8 - (5-x) =>
2x - x = 8-5+8 =>
x = 11
or
common difference
=2x-8
= 14
To find the common difference of an arithmetic progression, we need to look for the pattern in the consecutive terms.
In this case, we are given the consecutive terms of the arithmetic progression as 5-x, 8, 2x.
The common difference (d) is the difference between any two consecutive terms. Let's take the difference between the second term (8) and the first term (5-x):
8 - (5-x) = 8 - 5 + x = 3 + x
Now, let's take the difference between the third term (2x) and the second term (8):
2x - 8
Since the common difference should be the same in both cases, we can set up an equation:
3 + x = 2x - 8
Solving the equation for x:
3 + x = 2x - 8
x - 2x = -8 - 3
-x = -11
x = 11
Now that we have the value of x, we can substitute it back into one of the equations to find the common difference. Let's use the first equation:
3 + x = 3 + 11 = 14
Therefore, the common difference (d) of the arithmetic progression is 14.