SOLUTION: if we write the numbers from 1 to 201 what is the sum of all the odd numbers

Question 1119983: if we write the numbers from 1 to 201 what is the sum of all the odd numbers
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.

S =    1 +   3 +   5 +   7 + . . . + 201    <<<---=== 101 terms ! 

S =  201 + 199 + 197 + 195 + . . . +   1

---------------------------------------------------------------  Now add the two lines. Yoo will get

2S = 202 + 202 + 202 + 202 + . . . + 202 = 202*101 = 20200.


S =  =  = 10201.

---------------

Arithmetic progression with the first term 1 and the common difference 2.

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.

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