Unit 4 Exponential and Power Functions
Geometric Sequences Name_____________________
Day 2 Notes Date____________ Hour______
GEOMETRIC SEQUENCES
[pic]
Example 1: Is the given sequence geometric? If so, identify the common ratio.
A. 5, 15, 45, 135, … B. 15, 30, 45, 60, …
Example 2: Find the common ratio of each sequence. Then find the next term.
A. 12, 18, 27, 40.5 … B. 98, 14, 2 …
Example 3: Suppose you drop a ball from a height of 100 cm. It bounces back to
80% of its previous height. How high will it go after its fifth bounce?
Example 4: Find the 4th term in each geometric sequence
a. a7 = 4, r = [pic] b. a2 = -9, r = [pic]
[pic]
You can think of each term in the sequence as:
a1, a2, a3, a4, …, an-1, an, …
Example 5:
a. Write the recursive and explicit formulas for the geometric sequence with a1 = 6 and r = -2.
b. Write the 1st six terms of this geometric sequence. c. Find the 50th term of the sequence.
Example 6: Use the sequences to find the recursive formula and explicit formula.
A. 66, 33, 16.5, 8.25….. B. [pic]
a) Recursive b) Explicit a) Recursive b) Explicit
A. …, 28, ___, 5103 …
Example 7: Find the missing term in each geometric sequence.
B. …, 20, ____, 80 …
Homework: Day 2 Geometric Series Worksheet
-----------------------
The fixed amount multiplied by is called the common ratio, r. To find the common ratio, divide the second term by the first term.
If a sequence of values follows a pattern of multiplying each term by a fixed amount to arrive at the next term, then it is referred to as a geometric sequence. The number multiplied by is a constant.
In these formulas,
an is the nth term
a1 is the first term
n is the number of the term
r is the common ratio
Geometric Sequence Formulas
Recursive Formula Explicit Formula
a1 = a given value an = a1 " rn-1
an = an-1 " r
Next = Now " Common Ratio
GEOMETRIC MEAN = [pic]
∙ rn-1
an = an-1 ∙ r
Next = Now ∙ Common Ratio
GEOMETRIC MEAN = [pic]
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