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July 28th, 2014, 10:58 PM  #1 
Member Joined: Jun 2014 From: Brighton Posts: 49 Thanks: 2  Some formulas of Arithmetic progression/series
An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. Example: 2,4,6,8,10….. Arithmetic Series : The sum of the numbers in a finite arithmetic progression is called as Arithmetic series. Example: 2+4+6+8+10….. nth term in the finite arithmetic series Suppose Arithmetic Series a1+a2+a3+…..an Then nth term an=a1+(n1)d Where a1 First number of the series an Nth Term of the series n Total number of terms in the series d Difference between two successive numbers Sum of the total numbers of the arithmetic series Sn=n/2*(2*a1+(n1)*d) Where Sn – Sum of the total numbers of the series a1 First number of the series n Total number of terms in the series d Difference between two successive numbers Example: Find n and sum of the numbers in the following series 3 + 6 + 9 + 12 + x? Here a1=3, d=63=3, n=5 x= a1+(n1)d = 3+(51)3 = 15 Sn=n/2*(2a1+(n1)*d) Sn=5/2*(2*3+(51)3)=5/2*18 = 45 I hope the above formulae are helpful to solve your math problems. Last edited by skipjack; July 29th, 2014 at 03:48 AM. 
July 29th, 2014, 06:44 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
In a related note, you may find the gp command sumformal() useful. Let's say you want to find the sum of $3n^22n$. Just type Code: sumformal(3*n^22*n) Code: n^3 + 1/2*n^2  1/2*n 
August 6th, 2014, 03:29 AM  #3  
Member Joined: Jun 2014 From: Brighton Posts: 49 Thanks: 2  Quote:
 
August 6th, 2014, 09:58 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,469 Thanks: 2038 
As the nth number is a1 + (n  1)d, Sn = n(a1 + an)/2. Note that (a1 + an)/2 is the median of the n numbers, and is the "middle" number of the series if n is odd. It's slightly confusing to start by referring to a sequence of numbers and then keep switching between using the words "number" and "term". 

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n/2(2a1 (n1)d),sn=n/2(a1 an),Sn=N/2(2a1 (n1)d),a(n)=a1 (n1)d,arithmetic sn=n/2[2a1 (n1)d],sn=n/2(a1 an) explanation,sn=5/2[2a1,sn=n/2 [2a1 (n1)d],sum of an integers from 1 to 50 using sn=n/2[2a1 (n1)d],arithmetic series formula of sn=n/2 [2a1 (n1)d],Sn= n/2 [2a1 (n1)d],Sn=n\2[2a1 (n1)d],n℅2(2*120 (n1)*5 whic formula is this,n/2*(2*1 (n1)*5)=148 how?,sn=n/2 2a1 (n1)d
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