SOLUTION: What is the average of 1,2,3,4,5,6,7,8,9...2017 in simplest form? I don't know where to start because there are just too many numbers too add and divide by. Could anybody help?
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-> SOLUTION: What is the average of 1,2,3,4,5,6,7,8,9...2017 in simplest form? I don't know where to start because there are just too many numbers too add and divide by. Could anybody help?
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Question 1100151: What is the average of 1,2,3,4,5,6,7,8,9...2017 in simplest form? I don't know where to start because there are just too many numbers too add and divide by. Could anybody help? Answer by ikleyn(52905) (Show Source):
The sequense in this post is an arithmetic progression with the first term 1, the common difference 1, the last term 2017
and the number of terms 2017.
The sum of this progression is VERY WELL known: it is .
In order for to find "the average", you must to divide this sum by 2017, the number of terms.
Then you will get = 1009 for the average.
Notice, that 2018 is the sum of the first and the last term of this progression.
It is not accidentally:
The average of any arithmetic progression is the same as the average of its extreme terms.
