Sequences and Series Sequence : A list of numbers or objects in a special order. Example: 3, 5 7 9 , m,' ; ... is a sequence starting at 3 and increasing by 2 each time. Series : When you add the values in a sequence together, that sum is called a series. We have both finite and infinite series. Example: 3 + 5 + 7 +9 + ... is a series.
2
Finite and Infinite Sequences Finite sequence an It is series of n number of terms. Infinite sequence an, . It is series of infinite number of terms.
3
Sequences and Series Factorial Notation If n is a positive number, n factorial is defined as with 0 01=1 For example 4 , '2 '1=24
4
Sequences and Series Summation Notation The sum of the first n terms of a sequence is written as n
5
ل ر م ٠ ع - و ب ى
6
Arithmetic Progression Arithmetic Sequences A sequence is arithmetic if the difference between consecutive terms is constant, d is the common difference of the series. The sequence a a a a are said to be in
7
Geometric Progression Geometric Sequences A sequence is geometric if the ratio of consecutive terms is constant. a a a a a 4 a 3 r is the common ratio of the series. The sequence a a a , a 4 are said to be in
8
Infinite G.P. Series Geometric Series The sum of the terms in an infinite geometric sequence is called a geometric series. a + ar+ar + + Irl
Discussion
Copyright Infringement: All the contents displayed here are being uploaded by our members. If an user uploaded your copyrighted material to LearnPick without your permission, please submit a Takedown Request for removal.
Need a Tutor or Coaching Class?
Post an enquiry and get instant responses from qualified and experienced tutors.
If you have your own PowerPoint Presentations which you think can benefit others, please upload on LearnPick. For each approved PPT you will get 25 Credit Points and 25 Activity Score which will increase your profile visibility.