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Formula For The Sum Of Numbers Please

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devayaani | 09:07 Sun 25th Oct 2015 | Science
12 Answers
Hallo all,
I apologise in advance for asking the Maths question in Science section.

I tried to google to find the answer but could not find what I am searching for.
Can anyone tell me a formula to get the sum of consecutive numbers?

I know the Gauss formula for numbers starting from 1 to number “n”.

But my question is any consecutive numbers starting from any number. (Not starting from 1)
For example the sum of 76 + 77 + 78 + .....+ 98 = ??
Thanking you for help and once again apologies.
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http://www.wikihow.com/Sum-the-Integers-from-1-to-N

About half way down the page shows how to do from N1 to N2
((N+1)/2)*N)
Question Author
Thank you Sddsddean and Tora Tora Tora
Very much appreciated.
A useful closed form for the sum of consecutive numbers from n1 to n2 could be given by letting n2 = n1 + x, and then:

Sum = (x+1)n1 + x(x+1)/2 = (x+1)(n1+x/2)
Question Author
jim360
Thank you for the formula. Great help.

Quantity time Average value = Sum

Multiply quantity by average value to obtain sum of consecutive integers.

(Last - First) * (First + Last) / 2 = Sum
mibn2cweus - your formula should read:
(Last - First + 1) * (First + Last) / 2 = Sum

Thanks J-J

(Last - First + 1) gives the correct quantity of consecutive numbers.
Actually it should be -

(Last - First) + 1
the correct formula was given at 10:45.
No it wasn't ttt. If you read the question you'd see that your formula answers a different one.
Question Author
Thank you all for the formula.
I very much appreciate this help.

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