Arithmetic Series

In this page arithmetic series we are going to see ,how to find the sum of n terms in an arithmetic series.The formula,meaning of each term in that formula and also example problems with detailed steps.

The method used to find the sum of an A.P is known by Gaussian method of addition,named after German mathematician.Karl Friedrich Gauss(1777-1855 A.D). He found two formulas to find the sum of n terms to an Arithmetic progression.


1. Sequence is nothing but set of numbers.

2. Each number is separated by commas.


1.Series is nothing but sum of  terms.

2. Each number is separated by positive sign.

Now let us see the formula to find sum of n terms.

sn = n2 [2a + (n-1)d]

sn = n2 [a + l]

Here a = First term

        d = Common difference

        n = number of terms

        l = last term

Both are the formulas to find the sum of n terms.The first formula will be used if the last term is not given. However the last term is given we need to the second formula.

Some times if we are not given the number of terms in the series. We can find the number of terms by using the following formula.

n = (l-a)d + 1

Example 1:

Find the sum of the series 1 + 3 + 5 + .............+ 399


 Here we need to find the sum of the series  1 + 3 + 5 + .............+ 399

We don't know how many terms are in the series.So we have to use the formula to find how many terms are in the series.

The first term (a) = 1

Common difference (d) = 3-1

                               = 2

and the last term (l) = 399

  n =[ (399-1) / 2 ] + 1

  n = ( 398/2 ) + 1

     = 199 + 1

  n = 200

We have 200 terms in the arithmetic series.Here we have last term.So we can use the second formula.

sn = n2 [a + l]

  = [200/ 2(1 + 399)]

  = 100 (400)

  = 40000

Related Topics

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

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