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10 Mathematics notes Chapter 5 Arithmetic Progressions

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CBSE Class 10 Mathematics
NCERT Revision Notes
CHAPTER 05
ARITHMETIC PROGRESSIONS

Arithmetic Progressions
n^th Term of an AP
Sum of First n Terms of an AP
Miscellaneous Questions
Sequence: A set of numbers arranged in some definite order and formed according to some rules is called a sequence.
Progression: The sequence that follows a certain pattern is called progression.
Arithmetic Progression: A sequence in which the difference obtained by subtracting any term from its preceding term is constant throughout, is called an arithmetic sequence or arithmetic progression (A.P.).

The general form of an A.P. is a, a+d, a + 2d, ….. (a : first term, d = common difference).
The terms of A.P. is denoted by $a,{a_2},{a_3},........,{a_n}$ .

General Term: If ‘a’ is the first term and ‘d’ is common difference in an A.P., then ${n^{th}}$ term (general term) is given by ${a_n} = a + \left( {n - 1} \right)d$ .

Sum of n Terms of an A.P. : If ‘a’ is the first term and ‘d’ is the common difference of an A.P., then sum of first n terms is given by
${S_n} = \frac{n}{2}\{ 2a + (n - 1)\;d\}$
If ‘ $l$ ’ is the last term of a finite A.P. then the sum is given by ${S_n} = \frac{n}{2}\{ a + l\}$
(i) If ${a_n}$ is given, then common difference $d = {a_n} - {a_{n - 1.}}$
(ii) If ${S_n}$ is given, then ${n^{th}}$ term is given by ${a_n} = {s_n} - {s_{n - 1}}$
(iii) If a, b, c are in A.P., then 2b = a + c.
(iv) If a sequence has n terms, its ${r^{th}}$ term from the end $= {(n - r + 1)^{th}}$ term from the beginning.

Arithmetic Progressions class 10 Notes

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CBSE Class-10 Revision Notes and Key Points

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