Sum of Arithmetric Series

[Roundchild]

Hi! I hope I didn't put this into a wrong forum. Also, neither english nor math are my native language, so please have patience with me. I will do my best to explain the problem.

I need to make a formula in a Excel (I have Excel 2003), that takes value X and adds Z to it, then increases X by 1 and again adds Z to it, then again increases X by 1 and adds Z to it, until it reaches value Y plus Z.
Or, repeating the (X+1)+5 process N times.

For example, if X=3, Y=6 and Z=5:

(3+5)+(4+5)+(5+5)+(6+5)

X (and Y) will have to use values from 1 to up to tens of thousand. X, Y and Z (or X, Z and N) will be cell values from an existing table.

If this is possible to make in Excel in ANY way, I'd be extremely thankful to you for your solution.

Thank you in advance.

[DonkeyOte]

You can calculate the sum of an arithmetic series using:

(N(2a + ((N-1)*d)))/2

Where

N is number of terms - in your case this is 1+Y-X
a is first number in series - in your case this is X+Z
d is common difference of successive members - in your case 1

Thus if we assume X is A1 and is thus 3, Y is A2 and is thus 6 and Z is A3 and is thus 5 then the sum of the series can be calculated using:

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Altering values in A1:A3 will generate different results as required.

[zbor]

Here, try this formula:

=(Y-X+1)*(Y-X+2*Z)/2

(adjust cells related to upper numbers)

[Roundchild]

These work perfectly. Thank you for your patience and swift help!

[firefly2k8]

I think this is what you want. Although you may be able to use some theory to get the result instead.

Actually use the theory above.. this is overengineered.