SOLUTION: average of odd number up to 500

Question 885545: average of odd number up to 500
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
this should be an arithmetic series.
the total number of odd numbers start at 1 and go to 499.
the number 1 is the first number in the series.
the difference between each number is equal to 2.
the number 499 is the last number in the series.
the formula for the nth term of an arithmetic series is An = A1 + (n-1) * d
we know that A1 = 1
we know that d = 2
we know that An = 499
we can use the formula to find n which is the number of elements.
our formula of An = A1 + (n-1) * d becomes:
499 = 1 + (n-1) * 2
subtract 1 from both sides to get:
498 = (n-1) * 2
divide both sides by 2 to get:
249 = n-1
add 1 to both sides to get:
250 = n
the last term in the series is the 250th term.
now we can use the sum of an arithmetic series to find the sum.
the formula for sum of an arithmetic series is Sn = n * (A1 + An) / 2.
replacing n with 250 and A1 with 1 and An with 499 gets us:
Sn = 250 * (1 + 499) / 2 which becomes:
Sn = 250 * 500 / 2 which becomes:
Sn = 250 * 250 which becomes:
Sn = 62500
the average is equal to the sum divided by the number of elements which is equal to 62500 / 250 which is equal to 250.

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