The document discusses geometric sequences, defining them as lists of numbers where each term is generated by multiplying the previous term by a common ratio. It provides the formulas to calculate the common ratio, the nth term, and examples of finding specific terms within common geometric sequences. The document also includes an example word problem about calculating the amount of medicine in a cat's body over multiple days.

1. Sequences are everywhere ...
Photo source: Stone throw sequence

2. 3, 6, 12, 24, , ,

3. Geometric sequences on the calculator ...

4. Geometic Sequence:
(i) Recursive Definition: An ordered list of numbers
generated by continuously multiplying a value (the common ratio)
with a given first term.
(ii) Implicit Definition: An ordered list of numbers where each
number in the list is generated by an exponential equation.
Common Ratio (r):
(i) The number that is repeatedly multiplied to
successive terms in a geometic sequence.
(ii) From the implicit definition, r is the base of the exponential
function.

5. To Find The Common Ratio
r is the common ratio
tn is an arbitrary term in the sequence
t(n - 1) is the term immediately before tn in the sequence
To Find the nth Term In a Geometic Sequence
tn is the nth term
a is the first term
n is the quot;rankquot; of the nth term in the sequence
r is the common ratio

6. Once we know the pattern of a sequence, we can find any term of the
sequence. Use your calculator to check your answers.
Find the 110th term of: 5, 8, 11, 14, ...
U(110)= 332
Find the 21st term of: 3, 6, 12, 24, ...

7. Find the 27th term of: 1, 1, 2, 3, 5, 8, ...

8. Which term in the sequence: 2, 5, 11, 23, 47, ... is 1535?
HOMEWORK

9. My cat is sick. His name is Little John and he has a cold. The vet has
given him some medicine. Each day he gets a pill with 35 mg of
medicine. His body eliminates 25% of the medicine each day and then
he gets another pill. HOMEWORK
(a) How much medicine will be in his body in 5 days?
(b) Will the amount of medicine in his body stabilize? How many days
will it take and how much medicine will be in his body?