Section 8.3 Analyzing Geometric Sequences and Series Honors Algebra 2 Section 8.3 Analyzing Geometric Sequences and Series

Geometric Sequence- sequence where the ratio of any term to the previous term is constant Common ratio-constant ratio in a geometric sequence denoted by r

Geometric Sequence? #1 5, 1 5 , 1 25 , 1 125 #2 4, 16, 36, 64 #3 −8,−16,−32,−64 #4 2, 4, 6, 8, 10

The nth term of a geometric sequence with the first term being 𝑎 1 and the common ratio being r is 𝑎 𝑛 = 𝑎 1 𝑟 𝑛−1

Find the next three terms for each geometric sequence. #1 5, 15, 45 #2 8, 4, 2 #3 −6, 12, −24

Writing a rule! If you know the first term and the common ratio, you can find the rule by plugging the given info into the formula for the nth term. 𝑎 𝑛 = 𝑎 1 𝑟 𝑛−1

The graph of a geometric sequence would look very “exponential”- just dots If 𝑟>1, you are If 0<𝑟<1, moving on up you are going down

Writing a rule! Given :two terms Write an equation for each term Solve the system to find 𝑎 1 and r Write a rule for a geometric sequence that has 𝑎 5 =20 𝑎𝑛𝑑 𝑎 9 =131220

Geometric series-expression formed by adding the terms of a geometric sequence 𝑆 𝑛 denotes the sum of n terms The formula for the sum of the first n terms of a geometric sequence is 𝑺 𝒏 = 𝒂 𝟏 𝟏− 𝒓 𝒏 𝟏−𝒓

Find the sum 5 1 3 𝑖−1 Using the formula for sum.

Find the sum! 1 2 (5) 𝑘 How do I know this is geometric? 1 2 (5) 𝑘 How do I know this is geometric? Before you use the formula- Find the first term Find the common ratio

Another way! You can use the calculator to find geometric sums also!!! 𝑠𝑢𝑚(𝑠𝑒𝑞 .5× 5 𝑥 ,𝑥,1,10 )

Real-life College Loans You can calculate the monthly payment M (in dollars) for a loan using the formula 𝑴= 𝑳 𝟏 𝟏+𝒊 𝒌 Where L is the loan amount in dollars, i is the monthly interest rate (in decimal form), and t is the term (in months).

Katie is thinking about going to a four-year college and living in the dorms. If she goes to a two-year college and lives at home, she doesn’t have to borrow money. If she goes to the four-year college, she has to borrow $10,000 for each year. How big is her loan and what will she have to pay per month for the first ten years after graduation?

So many decisions!!! What is the total loan? This is L. t=120 Why? Interest 4% What does i equal?

After college!!! 𝑀= 40,000 1 1+0.04 𝑘 𝑀= 40,000 24.774088 𝑀=$1614.59 𝑀= 40,000 1 1+0.04 𝑘 𝑀= 40,000 24.774088 𝑀=$1614.59 You can use summation or the formula to get 24.774088

Calculate the monthly payment on a three-year loan for $10,000 with an annual interest rate of 12%.

Assignment #36 Pg. 430 #6-54 multiples of 3, 57,58