Notes On Sum of n Terms - CBSE Class 10 Maths
            

An A.P is a sequence of numbers or terms in which each term except the first one is obtained by adding a fixed number or constant to the term preceding term. 

The first term is denoted with ‘a’ and the fixed number is called the common difference denoted by ‘d’.

The common difference is the difference between two successive terms that is t2 – t1 = t3 – t2 = t4 – t3 =….

Sum of n terms of an AP
The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by
Sn = n 2 [ 2a + ( n - 1) d] or n 2 [ a + l ] or n 2 [ First term  + Last term]. where l = a + (n - 1) d is called the last term.

If Sn be the sum of first n terms of sequence and tn be the nth term of sequence can be written as,

nth term (tn) = Sn - Sn-1 and common difference(d) = an - an-1 = Sn - 2Sn-1 + Sn-2 .

            

Summary

            

An A.P is a sequence of numbers or terms in which each term except the first one is obtained by adding a fixed number or constant to the term preceding term. 

The first term is denoted with ‘a’ and the fixed number is called the common difference denoted by ‘d’.

The common difference is the difference between two successive terms that is t2 – t1 = t3 – t2 = t4 – t3 =….

Sum of n terms of an AP
The sum of first n terms of an AP with first term 'a' and common difference 'd' is given by
Sn = n 2 [ 2a + ( n - 1) d] or n 2 [ a + l ] or n 2 [ First term  + Last term]. where l = a + (n - 1) d is called the last term.

If Sn be the sum of first n terms of sequence and tn be the nth term of sequence can be written as,

nth term (tn) = Sn - Sn-1 and common difference(d) = an - an-1 = Sn - 2Sn-1 + Sn-2 .

            

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