Question 1150756
the formula for the nth term of an arithmetic progression is
:
a(n) = a +d(n-1), where a is the first term and d is the common displacement
:
we are given
:
a(3) = a+d(3-1) = 4x-2y
:
a(9) = a+d(9-1) = 10x-8y
:
solve each equation for a and then set them equal to each other
:
a +2d = 4x -2y
:
1)  a = 4x -2y -2d
:
a +8d = 10x -8y
:
2)  a = 10x -8y -8d
:
4x -2y -2d = 10x -8y -8d
:
-2d = 6x -6y -8d
:
6d = 6x -6y
:
d = x -y
:
The common difference is x-y
: