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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

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