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 ratiotn is an arbitrary term in the sequencet(n - 1) is the term immediately before tn in the sequence

To Find the nth Term In a Geometic Sequence

tn is the nth terma is the first termn is the "rank" of the nth term in the sequencer 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 21st term of: 3, 6, 12, 24, ...

Find the 110th term of: 5, 8, 11, 14, ...

U(110)= 332

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.

(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?

(a) How much medicine will be in his body in 5 days?

HOMEWORK