**Please Note: **
This article is written for users of the following Microsoft Excel versions: 97, 2000, 2002, and 2003. If you are using a later version (Excel 2007 or later), *this tip may not work for you*. For a version of this tip written specifically for later versions of Excel, click here: Finding the Sum of a Sequential Integer Range.

Written by Allen Wyatt (last updated August 20, 2020)**This tip applies to** Excel 97, 2000, 2002, and 2003

Excel includes the FACT worksheet function which returns the factorial of a value. (The factorial of the number X is the result of multiplying 1 * 2 * 3 ... * X.) Sabeesh wonders if there is a similar function that will return the sum of the values (1 + 2 + 3 ... + X) instead of the result of the values.

There is no such function built into Excel, but a quick mathematical formula will do the trick. The proper terminology to refer to this type of sum is a "triangular number." This derives from the fact that if the sum was represented with objects, they could always be arranged in the form of a triangle. For example, if you had 5 objects on the bottom row, 4 on the next, 3 three on the third, 2 on the fourth, and 1 on the top row, you have a triangle. Summing the number of objects (5 + 4 + 3 + 2 + 1) is what Sabeesh wants to do.

The answer to this problem can be expressed as a mathematical formula, reportedly discovered by Carl Friedrich Gauss. (Which is the source for another name of this type of number: a Gaussian Summation.) Note that the sum of opposite rows in the above example are always the same: 5 + 1 is the same as 4 + 2. This is true regardless of the number of rows; if there were 100 rows, then 100 +1 is the same result as 99 + 2, 98 + 3, 97 + 4, etc. What you end up with is 50 "pairs" of numbers equal to 1 more than the upper limit of your range.

The upshot of all this—without going through a lot of explanation—is that you can find the triangular number for any positive value (where you start at 1 and end with X) in the following manner:

=X*(X+1)/2

Thus, if you had a number in cell A1 and you wanted to know the sum of the range of 1 through that number, you could use this formula:

=A1*(A1+1)/2

This formula provides a simple way to determine the sum required, without the necessity of resorting to using a macro.

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This tip (9997) applies to Microsoft Excel 97, 2000, 2002, and 2003. You can find a version of this tip for the ribbon interface of Excel (Excel 2007 and later) here: **Finding the Sum of a Sequential Integer Range**.

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2023-12-31 16:18:13

Guy

I put it as n/2*(n+1) and tested it with 4 4/2*(4+1) which is 2.5*5 (10)

2021-07-04 02:56:10

Roy

Well, we'll have to wait... Some ignorant (yes, "ignorant" and also "thoughtless") "Flood" message came up. Done being helpful for today I guess.

2021-07-04 02:50:12

Roy

=SUM(SEQUENCE(1,26-8+1,8,1))

and cell addresses can be inserted for ending and starting values (26 and 8 above). One could use LET to place them at the absolute start of the formula for easy editing if one wishes them hardcoded rather than pulled from cells or formulas.

@Les McGarry: Similarly, your need could be served by using SEQUENCE inside INDIRECT to develop the addresses. That alone will produce an error though, but you can coerce the range to be used as desired by wrapping it in the SUM that you want to use anyway:

=SUM(INDIRECT("A" & SEQUENCE( ROWS(A1:A40)/4, 1, 1, 4)))

Notice using ROWS to get the number of rows in the range and then dividing by the "how many rows to move down by to get the next value" number (4 in this case). Just using ROWS by itself gets you 40 values and a wrong answer! The division by 4 (in this case) gets you exactly as many values a the sequence should get you so all is good.

2016-10-17 06:46:19

Michael (Micky) Avidan

Try:

=SUMPRODUCT((MOD(A1:A40,4)=1)*A1:A40)

--------------------------

Michael (Micky) Avidan

“Microsoft® Answers" - Wiki author & Forums Moderator

“Microsoft®” MVP – Excel (2009-2017)

ISRAEL

2016-10-17 01:58:38

Les McGarry

2016-04-27 05:49:34

Michael (Micky) Avidan

@Brandon,

Try my suggested 'Array Formula' in the following picture:

(see Figure 1 below)

--------------------------

Michael (Micky) Avidan

“Microsoft® Answers" - Wiki author & Forums Moderator

“Microsoft®” MVP – Excel (2009-2016)

ISRAEL

**Figure 1.**

2016-04-26 18:17:13

Brandon

2016-01-06 17:51:52

Rex

Thank you!

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