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Choi 2012

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What is a Sequence? A Sequence is a set of things (usually numbers) that are arranged in order, separated by a comma, and then put curly brackets {set bracket} around the whole thing. The first term is referred as, the second term as, the third term as, and so on. The term is referred to as. {4, 7, 10, 13, 16,...}

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Infinite & Finite Sequences If the sequence goes on forever it is called an infinite sequence. {1,2,3,4,...} {2,6,18,54,...} {a,b,c,d,e,...} If the sequence stops at certain point it is called a finite sequence. {1,3,5,7} {100,50,25}

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Example 1a – Explicit Formula Given the formula for the term, write the first 4 terms of each sequence and graph versus n. The first 4 terms are {1, 4, 7, 10} Explicit formula A formula for the nth term of a sequence, from which the terms of the sequence may be obtained by substituting 1,2,3,... And so on, in turn, for n in the formula.

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Example 1b Given the formula for the term, write the first 4 terms of each sequence and graph versus n. The first 4 terms are {2, 5, 10, 17}

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Example 2 – Formula for nth term Given the formula for the term in function notation, find. Given the formula for the nth term, tn or f(n), the terms of a sequence can be written by substituting term numbers for n.

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Example 3 – Finding Formula for the nth term a) Find the formula for the term that determines the sequence {4, 7, 10, 13,...}. a) Try to find the pattern 1 1 2 2 3 3 4 4 n n b) Use the formula to find and. 35 50 b) Recall: To determine the formula for the nth term of a sequence, find a pattern and use it to write an expression for each term as a function of its term number.

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Homework: P. 433 #1,2,4,7

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12.1 An Introduction to Sequences & Series

12.1 An Introduction to Sequences & Series

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