1.7 - Geometric sequences and series, and their applications. Use of the formulae for the nth term and the sum of n terms.

Geometric Sequence Info A sequence is geometric if the quotient between any term of the sequence and its previous term is constant. This constant is called the common ratio (r) of the sequence. r = = = = … u1 u2 u2 u3 u3 u4

Examples of Geo. Sequences 1, 2, 4, 8, 16, … r = = = = 100, -50, 25, -12.5… = = = = - 1 2 2 4 4 8 2 100 -50 -50 25 25 -12.5 2 1

More Examples In a geometric sequence u1 = 3 and the common ration is -2. Find u2 and u3. Solution: = -2  u2 = 3 u2 -6 -6 u3 = -2  u3 = 12 12 u4 = -2  u4 = -24

You try… In a geometric sequence, 𝑈 1 =3 and 𝑟=2. Find the 𝑢 4 & 𝑢 10 𝑢 4 =24 & 𝑢 10 =1,536

1st Period Geometric Project: Use the following geometric series and write a general formula (nth term): {1, 3, 9, 27, …} Write this formula using the terms 𝑈 𝑛 , 𝑈 1 , & 𝑟 (𝑐𝑜𝑚𝑚𝑜𝑛 𝑟𝑎𝑡𝑖𝑜) Also, using your GDC…graph the geometric function and describe the graph

The Geometric Sequence (nth Term) For any geometric sequence, the following formula will help you generate the general formula (nth term): 𝑈 𝑛 = 𝑈 1 𝑟 𝑛−1

Application of Geometric Sequences We saw that arithmetic sequences are line graphs, and now we learn that geometric sequences are exponential graphs. Let’s try one and see how we can set one up:

Homework Page 136 (Orange Book) Page 139 (Orange Book) Ex 5D.1 (1-5, 9 all & 10 (a only)) Page 139 (Orange Book) Ex 5D.2 (2-5 all)