Example: Finding the nth Term M3U1D4 Warm Up Find the 9th term of the geometric sequence 7, 21, 63, . . . a1 = 7 an = a1rn – 1 = 7(3)n – 1 a9 = 7(3)9 – 1 = 7(3)8 = 7(6561) = 45,927 The 9th term is 45,927. NEW SEATS!!!! Example: Finding the nth Term

Homework Check: 1150 283

Homework Check:

Collect Parent Letters Homework Check: Document Camera Collect Parent Letters

M3U1D4 Geometric Series Objective: To write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. F-BF.2

First Let’s Look at a Geometric Finite Series

WRITE THESE FORMULAS DOWN ON YOUR HINTS CARD!!! Vocabulary of Geometric Sequences and Series (Universal) FINITE!!! WRITE THESE FORMULAS DOWN ON YOUR HINTS CARD!!!

Example 1: Let’s Review Geometric Sequences and add!!! And S9 1/2 x 9 NA, yet… 2/3 Sn = )

Example 2: 1/2 7 x 127/128

Now Let’s Look at a Geometric Infinite Series

Let’s summarize what we know and add to it! 1, 4, 7, 10, 13, …. Infinite Arithmetic No Sum 3, 7, 11, …, 51 Finite Arithmetic 1, 2, 4, …, 64 Finite Geometric 1, 2, 4, 8, … Infinite Geometric r > 1 r < -1 No Sum Infinite Geometric -1 < r < 1

Example 3: Find the sum, if possible:

Example 4: Find the sum, if possible:

Example 5: Find the sum, if possible:

YOU TRY! Find the sum, if possible:

YOU TRY! Find the sum, if possible:

Example 6: Find n for the series in which 5 y x 440 3 Graph on positive window X = 16

Example 7: A Real World Example! An auditorium has 20 rows of seats. There are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. How many seats are there in all 20 rows? (n-1)

Example 8: The Bouncing Ball Problem – Version A A ball is dropped from a height of 50 feet. It rebounds 4/5 of it’s height, and continues this pattern until it stops. How far does the ball travel? 50 40 40 32 32 25.6 25.6 Notice…Drawing a Picture made visualizing and solving EASIER!!!

YOU TRY! The Bouncing Ball Problem – Version B A ball is thrown 100 feet into the air. It rebounds 3/4 of it’s height, and continues this pattern until it stops. How far does the ball travel? 100 100 75 75 225/4 225/4 REMEMBER…Drawing a Picture made visualizing & solving easier!!!

Finally, how can we evaluate these in the calculator???

Graphing Utility: Terms and Sum of a Sequence Graphing Utility: Find the first 5 terms of the geometric sequence an = 2(1.3)n. end value variable beginning value List Menu: Graphing Utility: Find the finite sum upper limit List Menu: variable lower limit Graphing Utility: Terms and Sum of a Sequence

Project UPDATE THE PERCENTAGES AS FOLLOWS: Don’t forget…. DUE Sept. 15th !!! See me personally if you’ve already started calculations

Classwork: U1D4 Back Side WS odds #1 reads:

Homework: Finish CW