8-5 Ticket Out 1. 2. 3.4. 5. 6.. 8-6 Geometric Sequences Obj: To be able to form geometric sequences and use formulas when describing geometric sequences.

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Presentation transcript:

8-5 Ticket Out

8-6 Geometric Sequences Obj: To be able to form geometric sequences and use formulas when describing geometric sequences.

Do you remember? What is an arithmetic sequence? A list of numbers where you find each new term by adding a fixed number to the previous term. 1, 7, 13, 19, 25, … +6 Common difference = 6 = d 31,37,43, …

Geometric Sequence A list of numbers where you find each new term by multiplying a fixed number to the previous term. 2, 10, 50, 250, … ×5 Common ratio = 5 = r 1250,6250,31250, …

So, what is the difference between arithmetic sequences and geometric sequences?

Arithmetic

a.3, 6, 12, 24, 48, 96, … b. … Geometric Sequence or Not? Example 1: Determine which of the following sequences are geometric. If so, give the value of r. ×2 r = 2 Yes! 1 ×½ Yes! r = ½

c.5, 10, 15, 20, … d.-6, -9, -12, -15, … Geometric Sequence or Not? Example 1: Determine which of the following sequences are geometric. If so, give the value of r. +5 No! -3 No! -3

What if we can’t find the common ratio? Divide the second term by the first. If that number gets you from the second term to the third, from the third to the fourth and so on, it is a geometric sequence and you found your ratio! 2, 4, 6, 8, 10, … 4 ÷ 2 = 2 4 × 2 ≠ 6 So, it is not a geometric sequence!

What if we can’t find the common ratio? Divide the second term by the first. If that number gets you from the second term to the third, the third to the fourth and so on, it is a geometric sequence and you found your ratio! 2, 4, 8, 16, 32, … 4 ÷ 2 = 2 4 × 2 = 8 So, it is a geometric sequence! 8 × 2 = 1616 × 2 = 32 r = 2

Finding the “nth” term of a Geometric Sequence First term Common ratio

Find that term! Example 2: Find the first, fourth, and eighth term of the following sequence. First Term:Fourth Term:Eighth Term:

Find the next three terms of the sequence 3, 6, 12, 24, … Find the next three terms of the sequence 4, 20, 100, 500, … Find the second, fifth, and seventh terms of the sequence A(n) = 3 (–2) n–1. Ticket Out

Homework p. 427 #1 – 23 odd