Class 10 Maths Arithmetic Progressions | Sum of first n terms of AP |

**Sum of first n terms of Arithmetic Progression**

Suppose a person gets a salary of 1000 Rs & an increment of 100Rs every month. We want to know how much salary the person has drawn in 10 months. For this we need to find sum of first 10 terms of this AP with a=1000 & d=100.

sum of the first n terms of an AP is given by **S = n/2 [2a + (n – 1) d]**

We can also write this as S = n/2 [a + a + (n – 1) d] = n/2 (a + a_{n} )

In the case above, n=10, a=1000, d= 100,

So, S = 10/2 [2*1000 + (10-1)*100] = 5*[2000+900] = 14500.

sum of first *n *positive integers is given by **S_{n} = n(n +1)/2**

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