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February 27th, 2012, 04:01 PM  #1 
Newbie Joined: Jan 2012 Posts: 28 Thanks: 0  Find the sum of the first 50 terms
Find the sum of the first 50 terms of the following sequence: 1 + 3  5 + 7 + 9  11 + 13 + 15  17 + ... 
February 27th, 2012, 05:36 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find the sum of the first 50 terms
We have the sum S given by: 
February 27th, 2012, 05:45 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find the sum of the first 50 terms
We could also write: S = 1 + 3  5 + 7 + 9  11 + ...  89 + 91 + 93  95 + 97 + 99 S = 99 + 97  95 + 93 + 91  89 + ...  11 + 9 + 7  5 + 3 + 1 Adding we get: 2S = 16(100 + 100  100) + 100 + 100 = 1800 S = 900 
February 27th, 2012, 05:56 PM  #4 
Senior Member Joined: Dec 2011 Posts: 277 Thanks: 2  Re: Find the sum of the first 50 terms
Mark looks like Carl Friedrich Gauss to me .

February 27th, 2012, 06:09 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Find the sum of the first 50 terms [attachment=0:21x2xpqg]gaussplate.jpg[/attachment:21x2xpqg] 
February 27th, 2012, 07:53 PM  #6  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039  Re: Find the sum of the first 50 terms Quote:
1 + 3 + 5 + 7 + ....... + 95 + 97 + 99 = 2500 2(5  11  17 .......  89  95) = 1600 Throwing that mess in the arithmetic series formula: 50(1 + 99) / 2  2[16(5 + 95) / 2] = 900  
February 28th, 2012, 03:38 AM  #7  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Find the sum of the first 50 terms Hello, stevecowall! And yet another approach . . . Quote:
 
February 28th, 2012, 08:40 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 21,026 Thanks: 2257 
The mean of the first 2 terms is 2. The mean of the first 5 terms is 3. The mean of the first 8 terms is 4. ... The mean of the first 50 terms is 18, so their sum is 900. 
February 28th, 2012, 12:59 PM  #9  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Re: Quote:
 

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