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Essential Question: What is a sequence and how do I find its terms and sums?. What is a sequence? How do I write a formula for a sequence? How do I find the terms of a sequence?. Sequence. An infinite sequence is a function whose domain is the set of positive integers.
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Essential Question: What is a sequence and how do I find its terms and sums? What is a sequence? How do I write a formula for a sequence? How do I find the terms of a sequence?
Sequence • An infinite sequence is a function whose domain is the set of positive integers. • The values are the terms of the sequence. • If the domain of the function consists of the first n positive integers only, the sequence is a finite sequence.
Infinite sequences go on forever. Finite sequences stop.
Ex. 1 Find the first four terms of the sequence First term Second term Third term Fourth term
Factorial 5! = 5 * 4 * 3 * 2 * 1 = 120 = 6 3! = 3 * 2 * 1
SUMMATION NOTATION Upper limit of summation (Ending point) SIGMA Lower limit of summation (Starting point)
SUMMATION NOTATION Upper limit of summation (Ending point) SIGMA Sum of the terms of a finite sequence Lower limit of summation (Starting point)
Infinite Sequence Infinite Series Finite Series or nth Partial Sum
Properties of sums (cont) • To find the sum of an infinite geometric series:
Find (a) the 3rd partial sum and (b) the sum Ex 8 (a) the 3rd partial sum
Find (a) the 3rd partial sum and (b) the sum Ex 8 (b) the sum
QUESTIONS? What are your Questions?