#### Revision Notes for Ch 5 Arithmetic Progression Class 10th Maths

**Arithmetic Progression**

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__: An arithmetic progression is a list of numbers in which each term is obtained by adding a fixed number d to the preceding term, except the first term.__

*Arithmetic Progression*__•__

__: The fixed number d is called the common difference of the A.P.__

*Term*•

__:__

*Common Difference**Each number in the list of arithmetic progression is called term. It can be positive, negative or zero.*

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*: If a is first term and d is common difference of an A.P. The general form of an AP is: a, a+d, a+2d, a+3d*__General form of an AP__
(iii) ax

^{3 }+ bx^{2 }+ cx + d is a polynomial of degree 3 cubic polynomial.
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__: We can find the nth term of an A.P by using T__*Finding General Term of an AP*_{n}= a + (n-1)d
We can find the required term by putting the numeric value of n(no. of term) which we have to find from starting.

**nth term from the end:**l - (n-1)d where, l is the last term

The number occurring at nth place is denoted by T

_{n}. The first term is T_{1 }, second term is T_{2 }and so on.__Common difference d__= T

_{ n-1 }- T

_{ n}

3, 7, 11, 15,19………….

This is an arithmetic progression which starts from 3. The common difference between two consecutive terms is 4.

That is

7-3=4, 11-7=4, 15-11=4

So, this is an AP with first term as 3, and common difference 4.

Or, we can say the AP is

3, 3+4, 3+4+4=3+2×4, 3+4+4+4=3+3×4

That is 4 is added to each term to get the next term.

**Arithmetic Mean**

If a,A, b are in AP we say that A is arithmetic mean between a and b. It is also written as AM

Let A is the AM between two numbers a and b

Let A be the AM between a and b, then

As we know that common difference is difference between two consecutive term of an AP, and it is same between two consecutive terms of the number.

So,

⇒A-a=b-A

⇒2A=b+a

A=(a+b)/2

So, arithmetic mean of a and b is (a + b)/2.

**Sum of n-terms of an AP**

Sum of n term of an AP is

Here n is number of terms of AP, a is first term and l is last term of the AP. Here, d is the common difference.

**Properties of Arithmetic Progression**

If a constant is added or subtracted or multiplied to each term of an A.P. then the resulting sequence is also an A.P.

If each term of an A.P. is divided by a non-zero constant then the resulting sequence is also an A.P.