Section 9.3 Geometric Sequences and series

1
Section 9.3 Geometric Sequences and series

• Objective
• How recognize a geometric sequence or series
• How to write geometric sequence rule
• How to find finite and infinite geometric sums

2

• Geometric Sequence multiplying each term by a
  common ratio (r).
• Example 3, 12, 48, r 4
• Example 100, 50, 25 r ½
• Formula
• nth term 1st term common ratio Term

3

• Find the next 3 terms of each geometric sequence.
• 1) 2)

4

• Find the next four terms of each geometric
  sequence.
• 3) 16, 24, 36, ____, ____, ____, ____
• 4) 162, 108, 72, ____, ____, ____, ____

54
81
121.5
182.25
48
32
21.3
14.2
5

• Find the nth term of each sequences.
• 5)
• 6)

1024
4
6

• Find geometric means.
• 7) 4, ____, ____, ____, 324

12
36
108
7

• Sigma Notation
• of term
• last term 1st term 1st term
  common ratio
• Example 8 5 10 20 40 to 7 terms
• 510204080160320
• 645

8

• Geometric Sum Formula for Series
• Sum of the nth terms 1st term common ratio
  nth term

9

• Find the sum of each geometric series.
• 9) 7 21 63 , n 10
• 10) 2401 343 49 , n 5

10

• Express each series in sigma notation and find
  the sum
• 11) 75 15 3 to 10 terms

11

• Sum of an Infinite Geometric Series
• -1 lt r lt 1
• Sum 1st term common ratio

12

• Find the sum of each infinite geometric series,
  if it exists.
• 12) 2/3 4/9 8/27

13

• Evaluate.
• 13)

14

• Evaluate.
• 14)

15
Assignment

• Page 640
• 3-36 multiples of 3, 51-90 multiples of 3,
  102-108 even