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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.
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There is a bunch of lessons on arithmetic progressions in this site:
- Arithmetic progressions
- The proofs of the formulas for arithmetic progressions
- Problems on arithmetic progressions
- Word problems on arithmetic progressions
- One characteristic property of arithmetic progressions
- Solved problems on arithmetic progressions
Also, you have this free of charge online textbook in ALGEBRA-II in this site
- ALGEBRA-II - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Arithmetic progressions".
Save the link to this textbook together with its description
Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson
into your archive and use when it is needed.