SOLUTION: if we write the numbers from 101 to 309 what is the sum of all the even numbers

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Question 1119991: if we write the numbers from 101 to 309 what is the sum of all the even numbers
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52852) About Me  (Show Source):
You can put this solution on YOUR website!
.
S = 102 + 104 + 106 + . . . + 308


is the sum of the arithmetic progression with the first term 102 and the common difference 2.


The number of terms is  %28308-102%29%2F2+%2B+1 = 104.


Now use the formula for the sum of an arithmetic progression


S = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An = %28%28102%2B308%29%2F2%29%2A104 = 21320.


Answer.  The sum under the question is 21320.

Solved.

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For introductory lessons on arithmetic progressions see
    - Arithmetic progressions
    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions
in this site.

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.


Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
That means, the sum 
102+104+106+108+....+306+308


General Term, 102%2B2%28n-1%29.

The series aske for is the sum from index 1 to 104 of 102%2B2%28n-1%29.