Home | | Maths 10th Std | Points to Remember

Numbers and Sequences | Mathematics - Points to Remember | 10th Mathematics : UNIT 2 : Numbers and Sequences

Chapter: 10th Mathematics : UNIT 2 : Numbers and Sequences

Points to Remember

Numbers and Sequences: Euclid’s division lemma, Fundamental theorem of arithmetic, Arithmetic Progression, Geometric Progression, Special Series

Points to Remember

Euclid’s division lemma

If a and b are two positive integers then there exist unique integers q and r such that a = bq + r, 0 ≤ r < |b|

Fundamental theorem of arithmetic

Every composite number can be expressed as a product of primes and this factorization is unique except for the order in which the prime factors occur.

Arithmetic Progression

(i) Arithmetic Progression is aa + da + 2da + 3d,….nth term is given by tn  = a + (n −1)d

(ii) Sum to first n terms of an A.P. is 

(iii) If the last term l (nth  term is given, then Sn   )

Geometric Progression

(i) Geometric Progression is aarar2 ,….,arn−1 . nth  term is given by tn= ar n−1

(ii) Sum to first n terms of an G.P. is 

(iii) Suppose r =1 then S n  = na

(iv) Sum to infinite terms of a G.P. a + ar + ar2 +  is   Where –1< r < 1

Special Series

(i) The sum of first n natural numbers 1 + 2 + 3 +  + n

(ii) The sum of squares of first n natural numbers


(iii) The sum of cubes of first n natural numbers 

(iv) The sum of first n odd natural numbers 1 + 3 + 5 + .... ..  + (2n − 1) = n2

 

Tags : Numbers and Sequences | Mathematics , 10th Mathematics : UNIT 2 : Numbers and Sequences
Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail
10th Mathematics : UNIT 2 : Numbers and Sequences : Points to Remember | Numbers and Sequences | Mathematics

Related Topics

10th Mathematics : UNIT 2 : Numbers and Sequences


Privacy Policy, Terms and Conditions, DMCA Policy and Compliant

Copyright © 2018-2024 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.