Warm-Up 1.Grab a worksheet off the stool. 2.Complete all of the odds.

Homework Check

Geometric Sequences and Series

What is a geometric sequence? In a geometric sequence, each term is found by multiplying the previous term by a constant.

What is a geometric sequence? In general you write a Geometric Sequence like this: {a, ar, ar 2, ar 3,... } Where a is the first term, and r is the factor between the terms called the common ratio. Example: a = 1 r = 2 Term#How it is written with “r” 1st11 2nd rd th

What do you notice? Do you see a pattern between term # and the exponent r is raised to? One less than the term number! Term#How it is written with “r” 1st22 2nd rd th th th

Formula a n = a 1 r (n-1) Where a n is the term we are looking for and a 1 is the first term in the sequence…so if we want to find the third term (a 3 ) we plug in 3 for n!

Look how we find each term… SequenceTermFormula a 1 r (n-1) Final Result 2a1a1 a 1 r (1-1) = 22 (1-1) 22 0 = 21 = 2 4a2a2 a 1 r (2-1) = 22 (2-1) 22 1 = 22 = 4 8a3a3 a 1 r (3-1) = 22 (3-1) 22 2 = 24 = 8 16a4a4 a 1 r (4-1) = 22 (4-1) 22 3 = 28 = 16 32a5a5 a 1 r (5-1) = 22 (5-1) 22 4 = 216 = 32 64a6a6 a 1 r (6-1) = 22 (6-1) 22 5 = 232 = 64

The graph…. We graph the order of the term for “x” and the number in that spot for “y” Term X Sequence Y Point 1st1(1,1) 2nd2(2,2) 3rd4(3,4) 4th8(4,8) 5th16(5,16)

Examples 1)What is the first term, a 1 ? What is the common ratio? Find the next 3 terms…. 1, 3, 27, ___, ___, ___ 2) What is the first term, a 1 ? What is the common ratio? Find the next 3 terms…. 70, 7, 0.7, ____, ____, ____

You Try 1)What is the first term, a 1 ? What is the common ratio? Find the next 3 terms…. -3, -6, -12, ___, ___, ___ 2) What is the first term, a 1 ? What is the common ratio? Find the next 2 terms…. 8, -20, 50, -125, ____, ____

Examples 3) Set up a geometric sequence with a 1 = 5, and the common ratio of 2. Find the 4 th term. 4) Set up a geometric sequence with a 1 = 7, and the common ratio of 1/5. Find the 3 rd term.

You Try 3 ) Set up a geometric sequence with a 1 = 6, and the common ratio of 3. Find the 4 th term using your formula. 4) Set up a geometric sequence with a 1 = 2, and the common ratio of ¼. Find the 3 rd term using your formula.

Examples 5) Find the first, fourth, and eighth term of each sequence. a n = 42 (n-1) 6 ) Find the first, third, and sixth term of each sequence. a n = (0.5)3 (n-1)

You Try 5) Find the first, fourth, and eighth term of each sequence. 6 ) Find the first, fifth, and seventh term of each sequence. a n = -2 5 (n-1) a n = (n-1)

Decide if each sequence is geometric or arithmetic….

Sum of A Finite Geometric Series Finite - having limits, something that is measureable. Finite Series - the sum of the terms of a sequence.sequence Geometric series -series in which the ratio of each two consecutive terms is a constant function of the sum.

Sum of A Finite Geometric Series Formula:

Example: 1. What is the sum of the first ten terms of the geometric series? ….

Example: -10 – 5 – 2.5 – … ; n = 7

You Try: …; n = 6

Homework Workbook pg. 13 #1-9 Extra Credit: Independent Practice Sheet: Evens, on separate sheet of paper. Due Friday March 20.