How do you sum an arithmetic series/sequence?

Is there a way to define and sum arithmetic sequences in Numbers?


Here's how I'm trying to apply it.


I have a value in one cell. In the next cell, I'm trying to write a formula to add all integers equal or lower than the value, stopping at 3. So if the value in the first cell is 9, the next cell returns 42 (9+8+7+6+5+4+3).


Can Numbers do this?

Posted on Aug 12, 2014 2:01 PM

Reply
2 replies

Aug 12, 2014 6:33 PM in response to jct101

Hi jct,


A quick google search landed me here:

http://www.wikihow.com/Sum-the-Integers-from-1-to-N

and gave me this formula to sum all integers from 1 to N:

(N(N + 1))/2

they also have an easy explanation as to how this formula works.

but you don't want to count 1+2 so you will have to subtract that.

Put the formula in your second cell with N being your first cell and you are done!


quinn

Aug 13, 2014 7:55 AM in response to jct101

There are a couple ways:

1) brute force:

2) elegant (t_quinns suggestion)



1) Brute force:


create a table with the a count in column A and the sum of the count in column B:

User uploaded file


B1=SUM($A$1:A1)


this is shorthand for... select cell B1, then type (or copy and paste from here) the formula:

=SUM($A$1:A1)


select cell B1, copy

select column B (click the "B" in the column header)

paste


2) The more elegant way is to use the formula t_quinn provided:

User uploaded file


type "the number" in cell D1 and enter the formula in E1.

E1=(D1×(D1+1))÷2

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How do you sum an arithmetic series/sequence?

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