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this should be an arithmetic series.
\n" ); document.write( "the total number of odd numbers start at 1 and go to 499.
\n" ); document.write( "the number 1 is the first number in the series.
\n" ); document.write( "the difference between each number is equal to 2.
\n" ); document.write( "the number 499 is the last number in the series.
\n" ); document.write( "the formula for the nth term of an arithmetic series is An = A1 + (n-1) * d
\n" ); document.write( "we know that A1 = 1
\n" ); document.write( "we know that d = 2
\n" ); document.write( "we know that An = 499
\n" ); document.write( "we can use the formula to find n which is the number of elements.
\n" ); document.write( "our formula of An = A1 + (n-1) * d becomes:
\n" ); document.write( "499 = 1 + (n-1) * 2
\n" ); document.write( "subtract 1 from both sides to get:
\n" ); document.write( "498 = (n-1) * 2
\n" ); document.write( "divide both sides by 2 to get:
\n" ); document.write( "249 = n-1
\n" ); document.write( "add 1 to both sides to get:
\n" ); document.write( "250 = n
\n" ); document.write( "the last term in the series is the 250th term.
\n" ); document.write( "now we can use the sum of an arithmetic series to find the sum.
\n" ); document.write( "the formula for sum of an arithmetic series is Sn = n * (A1 + An) / 2.
\n" ); document.write( "replacing n with 250 and A1 with 1 and An with 499 gets us:
\n" ); document.write( "Sn = 250 * (1 + 499) / 2 which becomes:
\n" ); document.write( "Sn = 250 * 500 / 2 which becomes:
\n" ); document.write( "Sn = 250 * 250 which becomes:
\n" ); document.write( "Sn = 62500
\n" ); document.write( "the average is equal to the sum divided by the number of elements which is equal to 62500 / 250 which is equal to 250.\r
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