1. Geometric Sequences

2. Warm Up What do all of the following sequences have in common? 1. 2, 4, 8, 16, …… 2. 1, -3, 9, -27, …. 3. 12, 6, 3, 1.5, …..

3. Graph the following sequences. The domain for each is {1, 2, 3, 4, …..} and range is the terms of the sequence. 1. 1, 2, 4, 8, 16, …… 2. 12, 6, 3, 1.5, ….. What type of function do you see?

4. Geometric Sequence If the generating function is exponential you have a geometric sequence. The first five terms of a geometric sequence are shown Starting with the first term, how do you get to the second term? From the second term, how do you get to the third? Etc…. What do you notice? This number is called the common ratio. N12345 anan 36122448

5. Geometric Sequence Given a geometric sequence with the first term a 1 and a common ratio f, we can write the generating function of the sequence where r is the common ratio.

6. Find the generating function for each of the following geometric sequences. 1. a 1 = 3, a 2 = 6 2. a 1 = 12, a 2 = 3 3. 5, -4, 3.2, -2.56, … 4. The 8 th term of 3, 1, 1/3, 1/9, ….

7. Finding the generating function when you are not given consecutive terms is a little tricky but can be done. Find the formula for the nth term of the geometric sequence with a 2 = 12 and a 5 = -768.

8. Find the generating function for the following geometric sequences. 1. a 3 = 20 and a 6 = -160 2.

9. Geometric Series Just like with arithmetic series we have a formula for adding up the first n terms of a geometric series.

10. Find sum of the following geometric series. Using the formula. 1. 2. 3. Find the sum of 4 + 12 + 36 + … + 2916