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.

**n ^{th} TERM OF AN A.P. :** It is denoted by t

_{n}and is given by the formula, t

_{n}= 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 a_{1} , a_{2}, , a_{n}, we have d= a_{k + 1} — a_{k} where a_{k + 1} and a_{k} are the (k+ 1)th and the kth terms respectively.

**SUM OF FIRST N TERMS OF AN A.P.**

It is represented by symbol S_{n} and is given by the formula,

S_{n}= n/2{ 2a + (n — 1)d} or, S_{n} = 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 — a_{n} = S_{n}— S_{n – 1}.

**TO FIND nth TERM FROM END OF AN A.P. : **

n^{th} 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 S_{n}= 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

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### Class 10 Exemplar Questions

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