Question 1025208
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The sum of the first two odd numbers is 1+3=4. The sum of the first three odd numbers is 1+3+5=9. What is the sum of the first eight odd numbers?  
How does a sum of the first eight even numbers compared to the sum of the first eight odd numbers? Explain why this is so?
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1.  I edited your post.


2.  The sum of the first n odd integer (positive) numbers is 
    1 + 3 + 5 + . . . + (2n-1) = {{{n^2}}}.   
    So, the sum of the first 8 odd integer (positive) numbers is {{{8^2}}} = 64.


3.  The sum of the first n even integer (positive) numbers is 
    2 + 4 + 6 + . . . + (2n) = n*(n+1).

    So, the sum of the first 8 even integer (positive) numbers is 8*9 = 72.


See the lesson <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A> (Problems 2 and 3) in this site.
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