Question

The third term of an Ap is 4m - 2n. If the ninth term of the progression is 2m - 8n. Find the common difference in terms of m and n.

A. 2m - 6n
B. 2m + 6n
C. 2m - 4n
D. 2m + 4n

Answer 1

The common difference in terms of m and n is 2m - 4n. The correct answer is C.

Step-by-step explanation:

To find the common difference in terms of m and n, we can use the given information from the arithmetic progression (AP). The third term is 4m - 2n, and the ninth term is 2m - 8n.

The formula for the nth term of an AP is given by: aₙ = a₁ + (n - 1)d

By substituting the values of the third term and ninth term, we get:

4m - 2n = a₁ + 2d

2m - 8n = a₁ + 8d

Solving these simultaneous equations, we find that the common difference is 2m - 4n. The correct answer is C.