Algebra 1 / Unit 7: Exponents and Exponential Functions
7.6 Geometric Sequences
Notes
A geometric sequence multiplies by the same common ratio $r$ each time: 3, 6, 12, 24, ... has $r = 2$.
- Explicit formula: $a_n = a_1 \cdot r^{n-1}$.
- Recursive formula: $a_1 = 3$, $a_n = 2 \cdot a_{n-1}$.
- A geometric sequence is an exponential function whose domain is the counting numbers.
Practice
What is the common ratio of $81, 27, 9, 3, ...$?
Each term is divided by 3.
For $a_n = 2 \cdot 5^{n-1}$, find $a_4$.
$2 \cdot 5^3 = 250$.
Which is geometric?
The ratio is $-2$ every time.
Ready for more? Take the Unit 7 test.