The 3rd term of an A.P is 4x - 2y and the 9th term is 10x - 8y. Find the common difference.
A
19x - 17y
B
8x - 4y
C
x - y
D
2x
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
n = 3, U\(_3\) = 4x - 2y,
U\(_n\) = a + (n-1)d,
4x - 2y = a + 2d... (1)
U\(_9\) = 10x - 8y,
10x - 8y = a + 8d... (2)
Solving (1) and (2),
subtract eqn i from ii
a-a + 8d - 2d = 10x -4x - 8y- (-2y)
6d = 6x - 8y+ 2y.
6d= 6x - 6y
6d = 6( x-y)
d = x - y
Source: Myschool Past Questions Archive (Record #582)