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Essential Question: What is a sequence and how do I find its terms and sums?

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?

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  1. 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?

  2. 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.

  3. Infinite sequences go on forever. Finite sequences stop.

  4. Ex. 1 Find the first four terms of the sequence First term Second term Third term Fourth term

  5. Find the first four terms of the sequence Ex. 2

  6. Factorial 5! = 5 * 4 * 3 * 2 * 1 = 120 = 6 3! = 3 * 2 * 1

  7. = (n+2)(n+1)n

  8. SUMMATION NOTATION Upper limit of summation (Ending point) SIGMA Lower limit of summation (Starting point)

  9. SUMMATION NOTATION Upper limit of summation (Ending point) SIGMA Sum of the terms of a finite sequence Lower limit of summation (Starting point)

  10. Ex. 7

  11. Ex 7b

  12. Infinite Sequence Infinite Series Finite Series or nth Partial Sum

  13. Properties of sums (cont) • To find the sum of an infinite geometric series:

  14. Find (a) the 3rd partial sum and (b) the sum Ex 8 (a) the 3rd partial sum

  15. Find (a) the 3rd partial sum and (b) the sum Ex 8 (b) the sum

  16. QUESTIONS? What are your Questions?

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