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### Formula for Sums of Counting Numbers

```Date: 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/
```
Associated Topics:
High School Number Theory

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