The \(3^{\text {rd }}\) term of an AP is \(4 x-2 y\) and the \(9^{\text {th }}\) term is \(10 x-8\). find the common difference.
A. \(x, y\) B. \(19 x-17 y\) C. \(2 x\) D. \(8 x-4 y\)
Correct Answer: A
Explanation
nth term of an AP. With first term ' \(a\) ' and common different ' \(d\) ' \(=a+(n-1) d\) \(3^{\text {rd }}\) term \(=4 x-2 y\) and \(9^{\text {th }}\) term \(=10 x-8 y\) \(=>a+2 d=4 x=2 y\) \(a+8 d=10 x-8 y\) subtract (i) from (ii) 6 d=6 x-6 yividing through by 6 , we get d=x-y
