Unit 1:Sequences & Series TestsStudent ID:
Day 7 –Geometric Sequences
Opener: Using any resources available, compare and contrast arithmetic means versus geometric means.
Geometric sequences are some of the most important sequences we study. They have the general form
Where is the scale factor and is the ______ratio. Re-write each sequence below so that it fits the general form of a geometric sequence. Then, identify the scale factor and the common ratio.
One of the most interesting facets of geometric sequences is that given any three consecutive terms (let’s call them and ), then is the geometric ______of and . Hence: geometric sequence!
Exploration: Using your calculator, graph each geometric sequence. Then, discuss what makes the sequence converge or diverge.
When does a geometric sequence converge? Diverge?Summary: A geometric sequence has the form
Complete the blank. Then, graph a general form of the sequence.
When , the sequence oscillates, meaning the sequence ______. / When , the sequence ______. / When , the sequence ______.How does affect your sequence?
Bookwork: p.618 #s 45 – 52
Practice Quiz
At this point, you should be fairly decent with sequences. The following practice quiz should be completed by next class. Show all work and DO NOT use a calculator unless otherwise mentioned.
Which of the following sequences converge?only / only / and / and / and
For which of the following does ?
only / only / only / and only / and only
Create an explicit rule for the given sequence, assuming
Create an explicit rule for the given sequence, assuming
Create an explicit rule for the given sequence, assuming
Create an explicit rule for the given sequence, assuming
Find the limit of the sequence if it converges. Otherwise, indicate divergence.
/ / / Diverges
Find the limit of the sequence if it converges. Otherwise, indicate divergence.
/ / / Diverges
Find the limit of the sequence if it converges. Otherwise, indicate divergence.
/ / / Diverges
Find the limit of the sequence if it converges. Otherwise, indicate divergence.
/ / / Diverges
Find the limit of the sequence if it converges. Otherwise, indicate divergence.
/ / / Diverges
is the sequence given below. To what number does converge?
/ / / / Diverges