Name: ____________________
F&PC 10/11H.
Period: _____________
Chapter 1 – Sequences and Series
Section 1.3 - Geometric Sequences
In geometric sequences each term is the previous term multiplied by a constant.
A geometric sequence is also called a geometric progression
Warm up – Suppose you have the geometric sequence 4, 12, 36, 108, …
a) What is t1?
b) What do you multiply by to get the next term (this is the r value)?
c) Is the sequence geometric (see the definition above)? In other words, is the r value
consistent throughout the sequence?
d) What is t5? Explain how you got t5.
e) Show how to get t5 using only t1 and r.
f) Show how to get t8 using only t1 and r.
g) What do you notice about the exponent on r compared to n?
h) Write a general formula for tn for any geometric sequence:
For a geometric sequence, the common ratio (r), can be found by taking any term (except
the first) and dividing that term by the preceding term. So r 
tn
tn 1
Example 1: Are the following sequences geometric (ie. Is the r value consistent)?
a) 2, 4, 6, 8
b) 4, 10, 25, 62.5
One way to represent any geometric sequence is t1, t1r, t1r2, t1r3,… etc.
n-1 integer is:
The general term
where3 n is a positive
So t1of=at1geometric
, t2 = t1r, tsequence
3 = t1r2. t4 = t1r , …, tn = t1r
OR
t1 is the first term, n is the number of terms, r is the common ratio, and tn is a general term
Example 2: Bacteria reproduce by splitting into two. Suppose there were three bacteria
originally present in a sample.
a) Determine the general term that relates the number of bacteria to the doubling
period of the bacteria. State the values of t1 and r in the geometric sequence formed.
b) How many bacteria will there be after 8 generations?
Example 3: Suppose a photocopier can make a 60% reduction on a picture. If the picture
is originally 42cm long, what length will it be after five successive 60%
reductions?
Example 4: In a geometric sequence, the second term is 28 and the fifth term is 1792.
Determine the values of t1 and r, and list the first three terms of the sequence.
Example 5: Two terms of a geometric series are a2  18 and a5  2 . Write a rule for the
3
n th term.
Assignment: Pg. 39-45
Q. # 1cde, 2c, 3c, 4, 5d, 6bc, 8, 9, 25