CBSE Class 10 Maths Arithmetic Progressions – Get here the Notes for CBSE Class 10 Maths Arithmetic Progressions. Candidates who are ambitious to qualify the CBSE Class 10 with good score can check this article for Notes. This is possible only when you have the best CBSE Class 10 Maths study material and a smart preparation plan. To assist you with that, we are here with notes. Hope these notes will help you understand the important topics and remember the key points for exam point of view. Below we provided the Notes of CBSE Class 10 Maths for topic Arithmetic Progressions.
- Class: 10th
- Subject: Maths
- Topic: Arithmetic Progressions
- Resource: Notes
CBSE Notes Class 10 Maths Arithmetic Progressions
Candidates who are pursuing in CBSE Class 10 are advised to revise the notes from this post. With the help of Notes, candidates can plan their Strategy for particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 10 Maths Arithmetic Progressions from this article.
SEQUENCE
A collection of numbers arranged in a definite order according to some definite rule (rules) is called a sequence.
Each number of the sequence is called a term of the sequence. The sequence is called finite or infinite according as the number of terms in it is finite or
infinite.
ARITHMETIC PROGRESSION
A sequence is called an arithmetic progression (abbreviated A.P.) if and only if the difference of any term from its preceding term is constant.
A sequence in which the common difference between successors and predecessors will be constant. i.e. a, a+d,a+2d
This constant is usually denoted by ‘d’ and is called common difference.
NOTE : The common difference ‘d’ can be positive, negative or zero.
SOME MORE EXAMPLES OF A PARE
(a) The heights (in cm) of some students of a school standing in a queue in the morning assembly are 147, 148, 149, ….. , 157.
(b) The minimum temperatures (in degree celsius) recorded for a week in the month of January in a city, arranged in ascending order are 3. 1, — 3. 0, — 2. 9, — 2. 8, — 2.7, — 2. 6, — 2. 5
(c) The balance money (in ) after paying 5% of the total loan of Z 1000 every month is 950, 900, 850, 800, ….50.
(d) The cash prizes (in ₹) given by a school to the toppers of Classes Ito XII are, respectively, 200, 250, 300, 350„ 750.
(e) The total savings (in ₹) after every month for 10 months when Z 50 are saved each month are 50, 100, 150, 200, 250, 300, 350, 400, 450, 500.
nth TERM OF AN A.P. : It is denoted by tn and is given by the formula, tn = a + (n —1)d
where ‘a’ is first term of the series, n is the number of terms of the series and ‘d’ is the common difference of the series.
NOTE : An A.P which consists only finite number of terms is called a finite A.P. and which contains infinite number of terms is called infinite A.P.
REMARK : Each finite A.P has a last term and infinite A.Ps do not have a last term.
RESULT: In general, for an A.P a1 , a2, , an, we have d= ak + 1 — ak where ak + 1 and ak are the (k+ 1)th and the kth terms respectively.
SUM OF FIRST N TERMS OF AN A.P.
It is represented by symbol Sn and is given by the formula,
Sn= n/2{ 2a + (n — 1)d} or, Sn = n/2 { a + l} ; where ‘l’ denotes last term of the series and l= a+(n-1)d
REMARK : The nth 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. — ie — an = Sn— Sn – 1.
TO FIND nth TERM FROM END OF AN A.P. :
nth term from end is given by formula l – (n – 1)d
nth term from end of an A.P. = nth term of (l, l — d, l – 2d,…….)
=l+(n-1)(—d)=l—(n-1)d.
PROPERTY OF AN A.P. :
If ‘a’ , b, c are in A.P., then
b — a= c — b or 2b= a + c
THREE TERMS IN A.P. :
Three terms of an A. P. if their sum and product is given, then consider
a—d,a,a+d.
FOUR TERMS IN A.P. :
Consider a —3d, a — d, a+ d, a +3d.
NOTE :
The sum of first n positive integers is given by Sn= n(n + 1) / 2
Class 10 Key Points, Important Questions & Practice Papers
Hope these notes helped you in your schools exam preparation. Candidates can also check out the Key Points, Important Questions & Practice Papers for various Subjects for Class 10 in both Hindi and English language form the link below.
| Class 10 Maths | कक्षा 10 गणित |
| Class 10 Science | कक्षा 10 विज्ञान |
| Class 10 Social Science | कक्षा 10 सामाजिक विज्ञान |
| Class 10 English |
Class 10 NCERT Solutions
Candidates who are studying in Class 10 can also check Class 10 NCERT Solutions from here. This will help the candidates to know the solutions for all subjects covered in Class 10th. Candidates can click on the subject wise link to get the same. Class 10 Chapter-wise, detailed solutions to the questions of the NCERT textbooks are provided with the objective of helping students compare their answers with the sample answers.
Class 10 Mock Test / Practice
Mock test are the practice test or you can say the blue print of the main exam. Before appearing in the main examination, candidates must try mock test as it helps the students learn from their mistakes. With the help of Class 10 Mock Test / Practice, candidates can also get an idea about the pattern and marking scheme of that examination. For the sake of the candidates we are providing Class 10 Mock Test / Practice links below.
Class 10 Exemplar Questions
Exemplar Questions Class 10 is a very important resource for students preparing for the Examination. Here we have provided Exemplar Problems Solutions along with NCERT Exemplar Problems Class 10. Question from very important topics is covered by Exemplar Questions for Class 10.
CBSE Class 10 Maths Notes Science Notes Social Science Notes English Notes
