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Geometric sequences. I’m teaching a quick (15 min) lesson. Then, we’re taking the quiz! (it’s only 10 questions). Please Pick Up A ½ Sheet Of Paper. Arithmetic Sequences. Geometric Sequences. ADD To get next term Have a common difference. MULTIPLY to get next term

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## Geometric sequences

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**Geometric sequences**I’m teaching a quick (15 min) lesson. Then, we’re taking the quiz! (it’s only 10 questions) Please Pick Up A ½ Sheet Of Paper**Arithmetic Sequences**Geometric Sequences • ADD To get next term • Have a common difference • MULTIPLY to get next term • Have a common ratio**In a geometric sequence, the ratio of any term to the**previous term is constant. You keep multiplying by the SAME number each time to get the sequence. This same number is called the common ratio and is denoted by r What is the difference between an arithmetic sequence and a geometric sequence? Try to think of some geometric sequences on your own!**Find r for the following sequences**4, 8, 16, 32... r=2 r=3 8, 24, 72, 216... r=4 6, 24, 96, 384... No common ratio! Geometric Sequence 5, 10, 15, 20...**Writing a rule**To write a rule for the nth term of a geometric sequence, use the formula:**Writing a rule**Write a rule for the nth term of the sequence 6, 24, 96, 384, . . .. Then find This is the general rule. It’s a formula to use to find any term of this sequence. To find , plug 7 in for n.**Writing a rule**Write a rule for the nth term of the sequence 1, 6, 36, 216, 1296, . . .. Then find This is the general rule. It’s a formula to use to find any term of this sequence. To find , plug 8 in for n.**Writing a rule**Write a rule for the nth term of the sequence 7, 14, 28, 56, 128, . . .. Then find**Writing a rule**(when you're not given the first term) One term of a geometric sequence is The common ratio is r = 3. Write a rule for the nth term.**Writing a rule**(when you're given two non-consecutive terms) One term of a geometric sequence is and one term is Step 1: Find r -divide BIG small -find the distance between the two terms and take that root. Step 2: Find . Plug r, n, and into your equation. Then, solve for . Step 3: Write the equation using r and .**Writing a rule**(when you're given two non-consecutive terms) Write the rule when and .**Graphing the sequence**Let’s graph the sequence we just did. Create a table of values. What kind of function is this? What is a? What is b? Why do we pick all positive whole numbers? Domain, Input, X Range, Output, Y**Think about it..**Does it make sense to connect the dots on our last graph? Why or why not? Work: Geo. Sequences W.S

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