SOLUTION: In a list of n consecutive odd numbers, the number of terms equals the first term. If six times the sum of the n numbers exceeds the square of their average by 2013 times the

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Question 1085838: In a list of n consecutive odd numbers, the number
of terms equals the first term. If six times the sum
of the n numbers exceeds the square of their average
by 2013 times the average, what is the value of the
first term?

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
In a list of n consecutive odd numbers, the number
of terms equals the first term. If six times the sum
of the n numbers exceeds the square of their average
by 2013 times the average, what is the value of the
first term?

S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29d%29
Average+=+S%5Bn%5D%2Fn%5E%22%22

consecutive odd numbers,
d+=+2

the number of terms equals the first term.
n=a%5B1%5D

Substituting those and simplifying


Average=S%5Bn%5D%2Fn%5E%22%22=n%282n-1%29%2Fn=2n-1

If six times the sum of the n numbers exceeds the
square of their average by 2013 times the average,
6n%282n-1%29=%282n-1%29%5E2%2B2013%282n-1%29

Divide through by (2n-1), which cannot be 0,
since n cannot be 1/2.

6n=%282n-1%29%2B2013

6n=2n-1%2B2013

6n=2n%2B2012

4n=2012

n=503

First term = a%5B1%5D=n=503

Edwin