# Sum of Arithmetic Progression – Sum of N terms Formula in Arithmetic Sequence

Sum of Arithmetic Progression – Sum of N terms Formula in Arithmetic Sequence

In previous video lessons we learned a lot about the sum of n terms of the Arithmetic progression –Sequences. I hope now you are good to deal all the problems related to nth term problems in Arithmetic Sequences.

Now in this video lesson we are going to learn a very important topic of arithmetic progression that is – Sum of Arithmetic Progression – Sum of N terms Formula in Arithmetic Sequence.

In this video lesson we will derive two formulas for the sum of arithmetic progression or simply formula for the sum of nth terms of an Arithmetic progression which are given by:

1. Sum of n terms of AP = [n {2a + (n-1)d} ] /2

2. Sum of n terms of AP = [n(a + l )]/2

Where a= first term of Arithmetic progression

n = total number of term in arithmetic progression

d = common difference

l = last term of Arithmetic progression

We use first formula when we get the first term(a), total number of terms (n) and common difference.

We use second formula when we know the last term(l), first term and common difference.

So how these formula came let’s start our lesson. I hope you are sitting with pen and notebook.

So how was it dear ?

Note 1 :-

In the formula , Sum of n terms of AP = [n {2a + (n-1)d} ] /2 there are four quantities namely sum of AP( Sn), a, n and d. If any three of these are known, the fourth can be easily determined. Sometimes two of these quantities are given, in such cases remaining two quantities are provided by some other relation.

Note 2 :

In the formula, Sum of n terms of AP = [n(a + l )]/2 there are again 4 variables or quantities depending on situation if you get any 3 you can easily calculate the 4th one.

Note 3 :

In the sum of n terms (Sn ) of a arithmetic sequence is given, then nth term of the arithmetic sequence can be determined by using the following formula:

Nth term = Sn – S(n-1) where S(n-1) = sum of (n-1) terms

I hope you understand the formula properly. Now on next video lessons we will learn problems based on the sum of arithmetic progression or sum of n terms of the arithmetic progression.

## Comments

## khan

hi men this video is not working please check,

do somthing.