SOLUTION: the sum of four arithmetic means between 2 and -10 is_____

SOLUTION: the sum of four arithmetic means between 2 and -10 is______

Question 1122290: the sum of four arithmetic means between 2 and -10 is______
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

Let the four arithmetic means be a, b, c, and d. Then the arithmetic sequence formed is

-10, a, b, c, d, 2

In that arithmetic sequence -- as in any arithmetic sequence -- the terms can be grouped in pairs with each pair having the same sum.

So the sum of the four arithmetic means is 2(-8) = -16.

In general, the sum of n arithmetic means between a and b is n times the average of a and b.

For this problem in particular, the average of the given two terms is (-10+2)/2 = -4; the sum of the four arithmetic means is 4(-4) = -16.
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