Formula for Sums of Counting NumbersDate: 09/19/2002 at 20:45:26 From: Kim Subject: Finding the Sums of counting numbers Can you please show and explain how this problem works out: 9+10+11...+60+61 and the question is to use the formula for the sum of the first n counting numbers to find the sum. I don't understand how you're supposed to do this problem. Please help! Kim Date: 09/19/2002 at 21:00:53 From: Doctor Robert Subject: Re: Finding the Sums of counting numbers Since the numbers form an arithmetic sequence, the way that you can find the sum is to find the average and then multiply by the number of numbers in the list. Finding the average is not as hard as it might sound. Since the numbers are in a sequence, to find the average of all of them you find the average of the first and the last. Example. 9+10+11 The average is (9+11)/2 = 10 The number of numbers is 3 so the sum is 3*10 = 30. 9+10+...+60+61 The average is (9+61)/2 = 35 There are (61-9)+1 = 53 numbers The sum is 53*35 = 1855 If you're into formulas, here it is: S(n) = (a(1)+a(n))/2 * n ...where n is the number of terms, a(1) is the first term, a(n) is the nth term. - Doctor Robert, The Math Forum http://mathforum.org/dr.math/ |
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