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

3, 6, 12, 24, , ,

Geometric sequences on the calculator ...

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.

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 \"rank\" of the nth term in the sequence
r is the common ratio

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, ...

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

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

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?