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