The sum of 40 A.M.’s between two number is 120. The sum of 50 A.M.’s between them is equal to?

Let "n" represent the number of arithmetic means between numbers A and B. Each "mean" will have a value A + k(B-A)/(n+1) for k=1, 2, ..., n. Then the sum of those n arithmetic means can be shown to be n(A+B)/2, which is proportional to n.
.. 50/40*120 = 150

The sum of 50 arithmetic means between the same pair of numbers will be 150.