Formula For The Sum Of Numbers Please

[devayaani]

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.

[sddsddean]

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

[ToraToraTora]

((N+1)/2)*N)

[devayaani]

Thank you Sddsddean and Tora Tora Tora
Very much appreciated.

[jim360]

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)

[devayaani]

jim360
Thank you for the formula. Great help.

[mibn2cweus]

Quantity time Average value = Sum

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

(Last - First) * (First + Last) / 2 = Sum

[Jonathan-Joe]

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

[mibn2cweus]

Thanks J-J

(Last - First + 1) gives the correct quantity of consecutive numbers.

[mibn2cweus]

Actually it should be -

(Last - First) + 1

[ToraToraTora]

the correct formula was given at 10:45.

[jim360]

No it wasn't ttt. If you read the question you'd see that your formula answers a different one.

[devayaani]

Thank you all for the formula.
I very much appreciate this help.