find the sum of n arithmetic means between x and 3x.
Answers
Step-by-step explanation:
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
If there are n means, then [x,3x] is divided into n+1 intervals.
If there are n means, then [x,3x] is divided into n+1 intervals.Thus, you have an arithmetic sequence where
If there are n means, then [x,3x] is divided into n+1 intervals.Thus, you have an arithmetic sequence wherea = x
If there are n means, then [x,3x] is divided into n+1 intervals.Thus, you have an arithmetic sequence wherea = xd = (3x-x)/(n+1) = 2x/(n+1)
If there are n means, then [x,3x] is divided into n+1 intervals.Thus, you have an arithmetic sequence wherea = xd = (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)
If there are n means, then [x,3x] is divided into n+1 intervals.Thus, you have an arithmetic sequence wherea = xd = (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
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