UNIT 1 - ARITHMETIC & GEOMETRIC SEQUENCES
Task #8 – You Tube Cat Video Problem (Geometric Series)
Common Core: HS.A-SSE.4, HS.F-BF.1, 2
MA40: ALGEBRA 2
Name:
Period:
INVESTIGATION
Cat Video on You Tube Problem: You video taped your cat doing
something extremely awesome and decided to post it on YouTube. You
told all your friends, so that on the first day your video was posted 2
people viewed it. The next day, each of your friends, both of them, had 3
friends each view the video. On the third day, each of those people had 3
friends view the video and this pattern continued. How many people
viewed the video on the 7th day? ... on the 14th day? One definition of a
“viral video” is if it gets a total of 5 million views in a 3-7 day period. Did
your cat video go viral?
1.
Sketch a series of pictures that illustrates what is happening in this
problem. Then, using words, describe the situation.
Pictures:
Words:
2.
Complete the table. Explain your method for completing the table.
Number
of Days
1
Number
of Views
2
2
Table Scratch Work:
Explanation:
3
4
5
6
7
...
...
14
Unit 1.8 – You Tube Cat Video Problem (Geometric Series) – (continued)
3.
How many people viewed the video on the 7th day? _______________
How many people viewed the video on the 14th day? ______________
4.
Did the video go viral? YES / NO (circle one)
Describe how you determined this. If you’re not sure, describe the
problem as you see it. Use pictures, tables, graphs, etc.
5.
Class Discussion – Let’s discuss how we can determine if the video
went viral.
6. Derive Formula for Finite Geometric Series
WRITE THE NEW EQUATION
n
a
i 1
(a)
1
 r i 1
USE THESE HINTS
Start with the sigma notation for Finite
Geometric Series.
a1 = 1st term, r = common ratio,
n = position of last term
Expand the series represented by
n
a
i 1
1
 r i 1 creating an equation.
Simplify the exponent on the common
ratio of each term.
(b)
n
Replace
a
i 1
1
 r i 1 . with S n .
(c)
Using the Multiplication Property of
Equality, multiply both sides of the
equation in (b) by the common ratio.
(d)
Simplify the exponent on the common
ratio in each term if it is not already
done.
We now have two equations. The equation in line (b) and the equation in line (d).
(e)
Write the equation from line (b).
(f)
Write the equation from line (d).
(g)
Subtract these two equations.
(h)
Simplify by eliminating the zero terms
if it is not already done.
(i)
Rewrite line (h) by using the
Distributive Property to factor both
sides of the equation.
Isolate
(j)
(k)
S n on one side of the
equation using the Multiplication
Property of Equality.
Use the Associative Property to
rewrite the equation so that the factors
involving the common ratio are
grouped as a fraction being multiplied
by the first term.
Unit 1.8 – You Tube Cat Video Problem (Geometric Series) – (continued)
Summary:
7.
Describe in words how the formula derived on the previous page can be
used to find the sum of the first n terms on a geometric series. Be
specific.
8.
When finding the sum of a geometric series, in addition to the formula
derived on the previous page, when will you need to use the formula
a n  a1  r n 1 ? Be specific.
9.
Find the sum of the geometric series 54  36  24  16  ... to 6 terms.