Algebra 1 - Exponential Functions

What is the common ratio?

In a geometric sequence, the ratio of successive terms is the same number r, or the common ratio.

When the terms in a geometric sequence alternate between positive and negative, is the value of r positive or negative?

Negative.

Find the next three terms in this geometric sequence. 2, 4, 6...

The common ratio is 2 (the previous number × 2 is the next number). So the next three terms are: 12, 24, 48...

Find the next three terms in this geometric sequence. 256, 64, 16...

The common ratio is ¼ (the previous number × ¼ is the next number). So the next three terms are 4, 1, and ¼...

When writing a function rule for a geometric sequence with a negative common ratio, do you put r in parentheses or not?

You do.

What is the equation for geometric sequences?

a sub n = a₁rⁿ⁻¹

The first term of a geometric sequence is 100, and the common ratio is 0.4. What is the 3rd term of the sequence?

a₃=100 (0.4)³⁻¹ a₃=100 (0.4)² a₃=100 (0.16) a₃= 16

The variable a is often used to represent terms in a sequence. What is it written as?

a₄

For a geometric sequence, a₁= 5, and r=2. What is the 7th term of the sequence?

a₇ = 5 (2)⁷⁻¹ a₇ = 5 (2)⁶ a₇ = 5 (64) a₇ = 320