The document discusses geometric sequences, which are patterns of numbers where each term is found by multiplying the previous term by a constant called the common ratio. It provides examples of geometric sequences with different common ratios and shows how to write equations to find the nth term in a sequence. It also explains how to find specific terms in a geometric sequence and calculates the geometric means between two nonconsecutive terms.

1. What comes next?
A geometric
3, 6, 12, 24 48 96
__, __, __ sequence is a
pattern of
x2 x2 x2 x2 x2 x2
numbers in
Common ratio which each
r=2 number is
a1 = 3 found by
multiplying a
a2 = 6 constant by the
number before
a3 = 12
it.

2. What’s the common ratio?
8, 4, 2, 1, …
r = 0.5
2, -6, 18, -54, … Alternating sequence
r = -3

3. 3, 6, 12, 24, 48, 96, …
x2 x2 x2
a1 = 3
a2 = 6 3 x 21
a3 = 12 3 x 22
a4 = 24 3 x 23
an = a1 x r (n – 1)

4. Write an equation for the nth term of the
geometric sequence 7, 14, 28, ….
an = a1 r (n – 1)
an = 7 2(n-1)
Find the 80th term of the sequence
an = 7 2 (n – 1)
a80 = 7 279

5. Complete the statement for the geometric sequence:
1536 is the ____ term of 3, 6, 12, …
an = a1 r (n – 1)
1536 = 3 2 (n – 1)
____ _
3 3
512 = 2(n – 1)
29 = 2(n – 1)
9=n–1
n = 10

6. The terms between any two nonconsecutive
terms of a geometric sequence are geometric
means.
Find the three geometric means between 12 and
3072.
12, ___, 192 768 3072, ...,
48 ___, ___,
xr xr xr xr
12 x r4 = 3072
r4 = 256
r=4