7 - 2: Geometric Sequences
Minds ON…The Sierpinski Triangle
For the following triangles, each white triangle is filled with an upside down black triangle.
1. Continue this process and complete the chart below.
Triangle Number, n
1
2
Number of White Triangles, W
1
3
3
4
5
n
2. Write a formula for the number of white triangles, W in terms of the triangle number, n.
Use your formula to find the number of white triangles in the 100th triangle in the sequence.
Generally, in a geometric sequence, the ratio of any term to the previous term is constant for all
pairs of consecutive terms. This constant is called the common ratio and is represented by r.
r
tn
t n 1
Ex. For the sequence 32, 16, 8, 4,… the constant ratio between consecutive terms is
The formula for the general term of a geometric sequence a, ar, ar2, ar3, … arn is:
t n  ar n 1
where,
tn =
n =
a =
r
=
Ex. 1: Identify which sequences are arithmetic, geometric or neither. Find the general term if
possible.
a) 4, 12, 36, 108, …
b) 100, 98, 96, 94
c) 32, 16, 8, 4, …
Ex. 2: Find the number of terms in the geometric sequence 6, 42, 294, … , 705894.
Ex. 3: Find the formula for the nth term and find t6 for the geometric sequence: 3, 6, 12, 24,…
Ex. 4: Find the general formula for the nth term of a geometric sequence if t3 = 99 and t5 = 11.
Homefun: p. 430 #1, 2 (omit recursive), 3 - 4, (6i, iii, 7, 10) odds, 11, 12, 14