Arithmetic Progressions

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NCERT Revision Notes for Chapter 5 Arithmetic Progressions Class 10 Maths

CBSE NCERT Revision Notes

1

Introduction

Answer

Sequence: It is set of numbers following an order, or a definite rule.
Progression: Sequences which follows a definite pattern are called progression.
Arithmetic Progression: 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. 
OR
The number occurring at nth place is denoted by Tn . The first term is T1 , second term is T2 and so on. 
Arithmetic  Progression is sequence when each term differs from its previous term by a constant. The constant is called common difference. 
Examples:-
3, 7, 11, 15,19………….............
This is an arithmetic progression which starts from 3. The common difference between two consecutive terms is 4. In an AP first term is represented as a, and common difference as d. 

2

Finding General Term  and Common difference of an AP

Answer

 We can find the nth term of an A.P by using Tn = 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 Tn . The first term is T1 , second term is T2 and so on.

Common difference d = T n-1 - T n

Examples:-

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.

3

Arithmetic Mean

Answer

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.

4

Sum of n-terms of An AP

Answer

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. 

5

Properties of Arithmetic Progression

Answer

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.

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