Featured Posts
Mathematics Assignments & Worksheets For Class IX Chapterwise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th to 12 th standard. Here students can find very useful content which is very helpful to handle final examinations effectively. For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapterwise assignments. These assignments cover all the topics and are strictly according to the CBSE syllabus. With the help of these assignments students can easily achieve the examination level and can reach at the maximum height. Class 09 Mathematics Assignment Case Study Based Questions Class IX
CBSE Class 10 Maths Formulas Chapter05  Arithmetic Progression
 Get link
 Other Apps
ARITHMETIC PROGRESSION
Class 10 Chapter 5
Class 11 Chapter 9
Sequence and Series

Sequence :
Example: 2, 4, 6, 10, 12, 14, ................
Series :
If the terms of a sequence are connected by plus (or minus) sign, is called a series.Example: 2 + 4 + 6 + 10 + 12 + 14 + ................
Progression:
A sequence following some definite rule is called a progression.Arithmetic Progression
A sequence is called arithmetic progression if the difference of a term and its previous term is always same.
A sequence a_{1}, a_{2}, a_{3 },_{ }a_{4}, _{ }a_{5} ………, a_{n }, a_{n+1 }……… is called arithmetic progression if a_{n+1} = a_{n} + d, where a_{1} is called first term and d is called the common
difference. 
3, 6, 9, 12, 15, ............
6  3 = 3, 9  6 = 3, 12  9 = 3, ..........t_{1}
Here we find that difference of any two consecutive terms is always remain same (3).
When difference of any two consecutive terms of a sequence remain same throughout the sequence, then that sequence is said to be in AP.
General Arithmetic Progression:
a , a + d, a + 2d, a + 3d, a + 4d +.............+ a + (n  1)d
Where
First Term(t_{1}) = a
Second Term(t_{2}) = a + d
Third Term(t_{3}) = a + 2d
..............................
.................................
Last term(t_{n}) = a + (n1)d
n^{th} term of sequence
is t_{n} = a + (n1)d Where common difference “d” is
given by: d = a_{n} – a_{n1} n^{th} terms of an AP from the end of the sequence is: l – (n1)d, where l is the last term of
the sequence. 
Finite Arithmetic Progression : When number of terms of an AP sequence are countable then AP is called Finite AP.
For example : 5, 10, 15, ............ 65.
Infinite Arithmetic Progression: When number of terms of an AP sequence are uncountable then AP is called infinite AP.
For example : 5, 10, 15, ...............
For example : 5, 10, 15, ............ 65.
Infinite Arithmetic Progression: When number of terms of an AP sequence are uncountable then AP is called infinite AP.
For example : 5, 10, 15, ...............
Here is a very interesting story related to the origin of this topic. Gauss was a great mathematician. When he was just 10 years old, teacher tell all the students of his class to add all the numbers from 1 to 100. He immediately replied that the answer is 5050. Can you guess, how did he do? We are here explain the method used by Gauss at that time : He wrote the numbers as follows S = 1 + 2 + 3 + ................... + 99 + 100 And then, reversed the numbers to write S = 100 + 99 + ................. + 2 + 1 Then he add both the sequences 2S = (100 + 1) + (99 + 2) + (98 + 3) + ............... + (2 + 99) + (1 + 100) 2S = 101 + 101 + 101 + .................... + 101 + 101 to 100 times 2S = 101 X 100 ⇒ If we take 100 = n, then n+1 = 101, So we can derive the formula for the sum of first n natural number With the help of above explanation we can derive the formula for finding the sum of n terms of an AP S = a + (a + d) + (a + 2d)+...................... + a + (n  1)d S = a + (n  1)d + [a + (n  2)d] +...............+ (a + d) + a Adding these two we get 2S = [a + a + (n  1)d] + [(a + d) + a + (n  2)d] + ................ + [a + (n  1)d + a] 2S = [2a + (n  1)d] + [2a + (n  1)d] + ........................... n times 2S = n X [2a+(n1)d] Sum of the first n terms of AP is Where "a" is the first term and "d" is the common difference of the given AP sequence. Sum of the first n terms of an AP is Where "a" is the first term and "l" is the last term of the given AP sequence. Sum of the first n terms from the end of the AP sequence is given by Sum of n even natural numbers is given by: Sum of first n odd natural numbers is given by 
Three terms in AP can be taken as : a  d, a, a + d
Four terms in AP can be taken as : a  3d, a  d, a + d, a + 3d
Five terms in AP can be taken as : a  2d , a  d , a , a + d , a + 2d
Six terms in AP can be taken as : a  5d, a  3d, a  d, a + d, a + 3d, a + 5dNOTE: Next topic is for the students after 10th standard in CBSE Board.
********************************************************
ARITHMETIC MEAN
If between two quantities a and b we have to insert n quantities A_{1}, A_{2}, A_{3}, A_{4},
………, A_{n} be such that A, A_{1}, A_{2}, A_{3}, A_{4},
………, A_{n}, b form an AP then we say that A_{1}, A_{2},
A_{3}, A_{4}, ………, A_{n }are n arithmetic means between
a and b
If a, b, c are in AP then middle term(b) is called the arithmetic mean and is given by
Explanation:
b  a = d and c  b = d
⇒ b  a = c  b
⇒2b = a + b
b  a = d and c  b = d
⇒ b  a = c  b
⇒2b = a + b
PROPERTIES OF A.P.
1) If a constant is added to or subtracted from each term of an A.P. , then the resulting sequence is also an A.P. , with the same common difference.
2) If each term of an A.P. is multiplied or divided by an nonzero constant k, then the resulting sequence is also an A.P. with common difference kd or d/k, where d is the common difference of the given A.P.
3)In a finite A.P. the sum of the terms equidistant from the beginning and end is always same and is equal to the sum of first and last term.
1) If a constant is added to or subtracted from each term of an A.P. , then the resulting sequence is also an A.P. , with the same common difference.
2) If each term of an A.P. is multiplied or divided by an nonzero constant k, then the resulting sequence is also an A.P. with common difference kd or d/k, where d is the common difference of the given A.P.
3)In a finite A.P. the sum of the terms equidistant from the beginning and end is always same and is equal to the sum of first and last term.
THANKS FOR YOU VISIT
PLEASE COMMENT BELOW
 Get link
 Other Apps
Breaking News
Popular Post on this Blog
Lesson Plan Maths Class 10  For Mathematics Teacher
ELESSON PLANNING FOR MATHEMATICS TEACHER CLASS 10TH lesson plan for maths class X cbse, lesson plans for mathematics teachers, Method to write lesson plan for maths class 10, lesson plan for maths class X, lesson plan for mathematics grade X, lesson plan for maths teacher in B.Ed. RESOURCE CENTRE MATHEMATICS LESSON PLAN (Mathematics) : CLASS 10 th Techniques of Making ELesson Plan : Click Here Click Here For Essential Components of Making Lesson Plan Chapter 1 : Number System This lesson plan is for the teachers who are teaching mathematics class 10 th For Complete Explanation Click Here New Lesson Plan with Technology Integration as suggested by CBSE in March, 2021 Class 10 Chapter 1 : Number System For Complete Explanation Click Here Chapter 2 : POLYNOMIALS This lesson plan is for the teachers who are teaching mathematics class 10 th For Complete Explanation Click Here Chapter 3 PAIR OF
Theorems on Quadrilaterals Ch8 ClassIX
Theorems on Parallelograms Ch8 ClassIX Explanation of all theorems on Parallelograms chapter 8 class IX, Theorem 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10, Mid point theorem and its converse. All theorems of chapter 8 class IX. Theorem 8.1: Prove that a diagonal of a parallelogram divides it into two congruent triangles. Given: In Parallelogram ABCD, AC is the diagonal To Prove: △ACD ≌ △ABC Proof: In △ACD and △ABC, ∠1 = ∠2 ......... (Alternate angles ∠3 = ∠4 .......... (Alternate interior angles AC = AC ........ (Common Sides ⇒ By ASA ≌ rule △ACD ≌ △ABC Theorem 8.2: In a parallelogram, opposite sides are equal. Given: ABCD is a parallelogram To Prove : AB = CD and BC = AD Proof: In △ ACD and △ ABC, ∠ 1 = ∠ 2 ......... (Alternate angles ∠ 3 = ∠ 4 .......... (Alternate interior angles AC = AC ........ (Common Sides ⇒ By ASA ≌ rule △ ACD ≌ △ ABC ⇒ AB = CD and BC = AD ….. By CPCT Theorem
Lesson Plan Math Class X (Ch13)  Surface Area and Volume
E LESSON PLAN SUBJECT MATHEMATICS CLASS 10 lesson plan for maths class 10 cbse lesson plans for mathematics teachers, Method to write lesson plan for maths class 4, lesson plan for maths class 12 rational numbers, lesson plan for mathematics grade 10, lesson plan for maths in B.Ed. Lesson Plan For CBSE Class 10 (Chapter 13) For Mathematics Teacher TEACHER'S NAME : SCHOOL : SUBJECT : MATHEMATICS CLASS : X STANDARD BOARD : CBSE LESSON TOPIC / TITLE : CHAPTER 13: SURFACE AREA & VOLUME ESTIMATED DURATION: This topic is divided into seven modules and are completed in twelve class meetings. PRE REQUISITE KNOWLEDGE: Perimeter and Area: Class VII Visualizing Solid Shapes: Class VII Visualizing Solid Shapes: Class VIII Mensuration: Class VIII Surface Areas and Volumes: Class IX Knowledge of unit conversion in mathematics TEACHING AIDS: Green Board, Chalk, Duster, Charts, solid figures, p