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Sequences & Series

Sequences & Series. Choi 2012. 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 ,

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Sequences & Series

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  1. Sequences & Series Choi 2012

  2. 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, ...}

  3. 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}

  4. Example 1a – Explicit Formula Given the formula for the term, write the first 4 terms of each sequence and graph versus n.  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. The first 4 terms are {1, 4, 7, 10}

  5. 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}

  6. 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.

  7. Example 3 – Finding Formula for the nth term a) Find the formula for the term that determines the sequence {4, 7, 10, 13, ...}. b) Use the formula to find and . a) Try to find the pattern b) Recall: 1 35 1 35 2 2 3 3 50 4 50 4 n n 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.

  8. Homework: • P. 433 #1,2,4,7

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