SOLUTION: Find the sum of the series 101+99+97+....+47.

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Question 1091469: Find the sum of the series 101+99+97+....+47.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
This sequence is an arithmetic progression with the first term 101, the common difference -2 and the last term 47.



The number of terms is %28101-47%29%2F2%2B1 = 28

    (in one more than the number of intervals of the length 2 between 101 and 47).



Now you can apply the formula for the sum of n terms of an AP:


S%5Bn%5D = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An = %28%28101%2B47%29%2F2%29%2A28 = %28148%2F2%29%2A28 = 2072.

Solved.


On arithmetic progressions see the lessons in this site:
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
    - Mathematical induction and 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".