Question

Find the sum of n' arithmetic means between x and 3x.

Answer 1

If there are n means, then [x,3x] is divided into n+1 intervals.

Thus, you have an arithmetic sequence where

a = x
d = (3x-x)/(n+1) = 2x/(n+1)

x, x + 2x/(n+1), x + 4x/(n+1), ... x + 2nx/(n+1), x + 2(n+1)x/(n+1)
= x, (n+3)/(n+1) x, (n+5)/(n+1) x, ... 3(n+1)/(n+1) x

Answer 2

Good