Class 11 Maths Sequences Series | Sum of first n terms of Arithmetic Progression |

**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] or **S = n/2 (a + a _{n} )**

Sum of first n positive integers is given by **S _{n} = n(n +1)/2**

**Arithmetic Mean**

Given two numbers a and b. We can insert a number A between them so that a, A, b is an A.P. Such a number A is called the arithmetic mean (A.M.) of the numbers a and b.

A.M. between two numbers a and b is their average or A = (a+b)/2

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

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

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