CBSE Class 10 Mathematics Arithmetic Progression Notes Set 03

CBSE Class 10 Mathematics - Arithmetic Progressions Concepts. Learning the important concepts is very important for every student to get better marks in examinations. The concepts should be clear which will help in faster learning. The attached concepts made as per NCERT and CBSE pattern will help the student to understand the chapter and score better marks in the examinations.

Class X

Chapter 5: Arithmetic Progressions

Chapter Notes

Top Definitions

1. 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.

2. The difference between the two successive term of an A.P is called the common difference.

3. Each of the number in the list of arithmetic progression is called a term of an A.P

4. The arithmetic progression having finite number of terms is called a finite arithmetic progression.

5. The arithmetic progression having infinite number of terms is called an infinite arithmetic progression.

Top Concepts

1. A list of numbers a¹, a², a³…… is an A.P, if the differences a₂–a₁, a₃–a₂, a₄–a₃ … give the same value i.e a_k+1 – a^k is same for all different values of k.

2. The general form of an A.P is a, a+ d, a+ 2d, a+3d…..

3. If the A.P a, a+d, a+ 2d……… l is reversed to l , l -d, l -2d………a, then the common difference changes to negative of original sequence common difference.

4. The n^th term of an A.P is the difference of the sum to first n terms and the sum to first (n-1) terms of it. i.e a_n=s_n-s_n-1

Top Formulae

1. The general term of an A.P is given by:

a_n = a + (n-1)d where a is the first term and d is the common difference.

2. Sum of n terms of an A.P is given by:

S_n=2/n[2a +(n -1)d]

where a is the first term, d is the common difference and n is the total number of terms.

3. Sum of n terms of an A.P is also given by:

Sn = n/2 [ a + l ] 

Where a is the first term and l is the last term.

4. The general term of an A.P l , l -d, l -2d…….. is given by:

a = l + (n-1)(-d)

where l is the last term, d is the common difference and n is the number of terms.

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