**Arithmetic Progression Class 10 Maths, deals with various concepts which are as under:-**

- Arithmetic Progressions
- nth Term of an AP
- Sum of First n Terms of an AP

### 1. Arithmetic Progression

#### Introduction of Arithmetic Progression, First term and Common Difference

Arithmetic Progression is a series of numbers, in which each successive termis obtained by adding a fixed number to the preceding term except the first term. that fixed term is known as common difference, which can be positive or negative.

### 2. nth term of an AP – Arithmetic Progression Class 10

If 1st term = a

Common difference = d

we know that for an AP

#### Finding first 5 terms of an Arithmetic Progression when first term and common difference are given?

#### Determining whether given data forms an AP?

#### Find Common Difference – 1st and 6th term of Arithmetic Progression given

#### Finding the missing terms of an Arithmetic Progression

#### Find ranking of a term in an Arithmetic Progression

#### First negative term in an Arithmetic Progression

#### Number of multiples of given number in Arithmetic Progression

#### Finding the salary in Year 10 Arithmetic Progression

#### Correlation between terms of an Arithmetic Progression given – Finding AP

### 3. Sum of n terms of an AP – Arithmetic Progression Class 10

a + (a + d) + (a + 2d) + (a + 3d)…………. + (a + (n – 1)d) = S ……………………. (1)

(a + (n – 1)d) + ……………………………+ (a + d) + a = S ……………………………….(2)

Add equation 1 and 2. We will get

2S = n{2a + (n – 1)d}

S = Sum of n terms of an AP = n/2{2a+(n-1)d}

#### Sum of an Arithmetic Progression

#### Finding Sum of Arithmetic Progression upto given number of terms

#### 1st and last term of Arithmetic Progression and Sum thereof

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

Because we know that nth term of AP = a + (n – 1)d

nth term of an AP = Difference between the sum of n terms and sum of (n – 1)terms

#### Total Cost of tractor including interest – Arithmetic Progression problem 1