Advanced Precalculus Notes 11.3 Geometric Sequences; Geometric Series

Advanced Precalculus Notes 11.3 Geometric Sequences; Geometric

Series

A geometric sequence (progression) has a constant ratio. Recursive Explicit

1

1

nn raa

aa 11

nn raa

Is the sequence 2, 6, 18, 54, 162, . . . a geometric sequence?

Show that the sequence is geometric. Show that the sequence is geometric.

nns

2}{

}4{}{ nnt

Given the geometric sequence: a) Find the 9th term. b) Find a recursive formula for this sequence.

100

729,

10

81,9,10

Sum of a Geometric Sequence: Find the sum of n terms of the sequence:

1,01

11

rr

raS

n

n

n

2

1

Use the calculator to find the sum of the first 15 terms of the sequence:

n

3

1

r

ara

k

k

11

11

Find the Sum of the geometric series:

9

8

3

42

Show that the repeating decimal 0.999. . . equals 1.

Initially, a pendulum swings through an arc of 18 inches. On each successive swing, the length of the arc is 0.98 of the previous length. a) What is the length of the arc of the 10th swing? b) On which swing is the length of the arc first less that 12 inches? c) After 15 swings, what total distance will the pendulum have swung? d) When it stops, what total distance will the pendulum have swung?

Assignment: page 856: 1 – 4, 7, 15, 18, 23, 29, 37, 34, 37, 43, 49, 55, 69, 71