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.
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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.
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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
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Sequences and Series Summation Notation The sum of the first n terms of a sequence is written as n
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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
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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
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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
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