Download The Length of a Line Segment

Pre-Calculus 11
Date: _____________________
Page 1 of 4
Section 1.3: Geometric Sequences
We are going to investigate a new type of pattern by using a sticky note and ruler. Fold this piece of
paper in half, given 2 layers of paper. Then fold it in half again, and continue to fold in half as long as
you can. Record your results below in the table.
Number of folds
Number of layers
0
1
Area of rectangle created (use inches)
1
2
3
4
What type of pattern do you see for…
a) the number of layers ______________________________________
b) area of rectangle created __________________________________________.
The sequences created by these patterns forms ____________________ sequences. In a geometric
sequence, the ratio formed by DIVIDING any term by the preceding term is called the
____________________. In this example, the common ratio for the number of layers is ________ and
the area of the rectangle created is ________.
Investigate: Let’s see if we can create a formula for finding t n of a geometric sequence 10, 20, 40…
Terms
Value of the
Value expressed using first
Algebra Representation
nth term
term & common ratio
using t1 and r
t1 (first term)
t 2 (second term)
t 3 (third term)
t 4 (fourth term)
t n (the nth term)
The general term of an GEOMETRIC sequence is given by
where:
t1 = _____________________
d = _____________________
n = _________________________ t n = _______________________________
Pre-Calculus 11
Section 1.3: Geometric Sequences
Date: _____________________
Page 2 of 4
Example 1: For each geometric sequence, write a formula for t n and use it to find each term.
3
a) -3, 15, -75, 375, … find t 8
b) 12, 6, 3, ,… find t12
2
Example 2: Mr. Lee often uses the school photocopier to reduce the size of pictures. Suppose the
smallest reduction the photocopier could make is 64% of the original. What is the shortest possible
length after 7 reductions of a photograph that is originally 45 cm long?
Example 3: The second term of a geometric sequence is 8 and the fifth term is 512. Find the first term.
Pre-Calculus 11
Section 1.3: Geometric Sequences
Date: _____________________
Page 3 of 4
Example 5: A ball is dropped from a height of 2 metres. After each bounce, it rises to 70% of its
previous height.
a) What height does the ball reach after 5 bounces?
b) After how many bounces does the ball reach a height of only 20 cm?
Pre-Calculus 11
Section 1.3: Geometric Sequences
Date: _____________________
Page 4 of 4
Example 5: Insert three numbers between 4 and 324 so that the terms form a geometric sequence.
Example 6: A doctor prescribes 200 milligrams of medication on the first day of treatment. The
dosage is reduced by 40% on each successive day for one week. How much medication does the
patient get on the last day of the week? Express your answer to the nearest tenth of a milligram.