Some formulas of Arithmetic progression/series

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burgessjohn
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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+(n-1)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+(n-1)*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=6-3=3, n=5
 
x= a1+(n-1)d = 3+(5-1)3 = 15
 
Sn=n/2*(2a1+(n-1)*d)
Sn=5/2*(2*3+(5-1)3)=5/2*18 = 45
 
I hope the above formulae are helpful to solve your math problems
 
 
Thanks