10.7 Geometric Series Notes.notebook
Bellwork
Write an explicit formula and recursive formula for the sequence. 2, ­6, 18, ­54 . . .
Jan 24­2:06 PM
February 24, 2016
10.7 Geometric Series
Objectives:
TSW: 1. Build a geometric series using the explicit formula
2. Find the sum of a finite and infinite geometric series Nov 26­9:35 AM
Example 1: The deer population is an area is increasing. This year, the population was 1.025 times last year's population of 2537. Geometric:
A sequence that has a common ratio.
a) Assuming the population increases at the same rate for the next few years, write an explicit formula for the sequence. Explicit Formula:
b) What will the deer population be for year four?
Recursive Formula:
Nov 26­9:35 AM
Sum of a finite geometric series c) Each year, the forestry service will tag each deer in this area for tracking purposes. How many tags will the forestry service need to tag each deer for the entire four years?
Nov 26­9:35 AM
d) Determine how many tags would be needed over the next ten years to tag each deer in their growing population.
Sn = the sum of the series
a is the first term
r is the common ratio
n is the nth term
Nov 26­9:35 AM
Nov 26­9:35 AM
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10.7 Geometric Series Notes.notebook
Example 2: The tallest totem pole carved from a single log is 38.28m high and is in Beacon Hill Park in Victoria B.C. If a lacrosse ball is dropped from this height and bounces back up 60% of the original height, find the total distance travelled by the ball by the time it hits the ground for the tenth time? February 24, 2016
Sum of an Infinite Geometric Series
S = the sum of the series
a is the first term
r is the common ratio
Dec 1­11:03 PM
Example 3: Determine the sum of the following infinite geometric series:
a) 27, 9, 3, 1, . . .
Dec 1­11:03 PM
Assignment
10.7 Worksheet
b) , . . . Dec 1­11:03 PM
Dec 1­5:05 PM
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