Google Answers Logo
View Question
 
Q: Excel Formula Question ( Answered,   3 Comments )
Question  
Subject: Excel Formula Question
Category: Computers > Algorithms
Asked by: boschdog-ga
List Price: $20.00
Posted: 27 Jun 2006 19:21 PDT
Expires: 27 Jul 2006 19:21 PDT
Question ID: 741617
I am trying to create a "simple" formula in an excel cell that reads any
number, ex. the number 8, and computes the following
=(+1+2+3+4+5+6+7+8)with the result being 36 or number 31
=(+1+2+3+4+5+6+7+8...+31)with the formula result of 496.  I am not
looking for a
formula that just sums up the logical series of a sequential list of
numbers, i.e. =sum(A1:A31) with cell A1 being 1 , A2 being 2, and so
on.
Answer  
Subject: Re: Excel Formula Question
Answered By: tox-ga on 27 Jun 2006 20:10 PDT
 
Hi there boschedog-ga,

What you are looking for is the formula for an arithmetic series (an
arithmetic series is the sum of an arithmetic sequence).  We call a
sequence of numbers an arithmetic sequence if the difference of any
two consecutive term is the same.  An example is a sequence of odd or
even numbers, in which case the common difference is 2, or the
sequence of natural numbers which you listed in your question, in
which case the difference is 1.

Now let's get right to the point.
Assuming that you have a number, eg 8, in cell A1, the formula for the
sum would be:  =A1*(A1+1)/2

There are a few ways to understand why this is so.
First method:
Assume that the number you have is "n".
So, you're looking for 1 + 2 + 3 +...+ (n-2) + (n-1) + n.  Let's call
this sum, "S".
Write out the sequence again below it, but in reverse order and add them.
   S =   1   +   2   +   3   + ... + (n-2) + (n-1) +   n
   S =   n   + (n-1) + (n-2) + ... +   3   +   2   +   1
--------------------------------------------------------------
 S+S = (n+1) + (n+1) + (n+1) + ... + (n+1) + (n+1) + (n+1)

Now, we can see that the left side is equal to 2S since we just added
the same series to itself.  On the right side, you see that every pair
of terms add up to (n+1).  We also know that there are n pairs of
(n+1) since S has n terms.
Thus 2S = (n+1)*n
S = n(n+1)/2

Second method:
If you want to see a graphical interpretation of the sum, please check
out this link:
http://merganser.math.gvsu.edu/calculus/summation/arithmetic.html


I hope this has helped and please feel free to ask for any
clarification and I'd be happy to help you further.  The formula for
different arithmetic series (where the difference between the terms
isn't 1) requires slight adjustment but can be derived in the same way
- please let me know if you require the general formula.

Cheers,
Tox-ga
Comments  
Subject: Re: Excel Formula Question
From: kottekoe-ga on 27 Jun 2006 19:43 PDT
 
N*(N+1)/2
Subject: Re: Excel Formula Question
From: kaixinhahaha-ga on 27 Jun 2006 20:46 PDT
 
N*(N+1)/2

this
Subject: Re: Excel Formula Question
From: tomhawk-ga on 06 Sep 2006 14:26 PDT
 
=(A1*(A1+1))/2   paste this in cell A3 put value in A1 that u need 

like if no is 5 put in A1 u will get value in A3 

**** a beginner can understand beginner well****

:) :) :) :) :)

Important Disclaimer: Answers and comments provided on Google Answers are general information, and are not intended to substitute for informed professional medical, psychiatric, psychological, tax, legal, investment, accounting, or other professional advice. Google does not endorse, and expressly disclaims liability for any product, manufacturer, distributor, service or service provider mentioned or any opinion expressed in answers or comments. Please read carefully the Google Answers Terms of Service.

If you feel that you have found inappropriate content, please let us know by emailing us at answers-support@google.com with the question ID listed above. Thank you.
Search Google Answers for
Google Answers  


Google Home - Answers FAQ - Terms of Service - Privacy Policy