**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

–=d

⇒=d+=d+a

Similarly =d+ =d+d+a = 2d + a

So =d+=(n-1)d+a

### 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+}

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

= –

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