Recognizing and Extending Geometric Sequences
Identify and extend Recognizing and Extending Geometric Sequences in Grade 9 algebra. Calculate terms, find the nth term formula, and apply sequences to real-world patterns.
Key Concepts
New Concept A geometric sequence is a sequence with a constant ratio between consecutive terms. What’s next Next, you’ll practice finding the common ratio and use it to extend sequences and calculate any term with a powerful formula.
Common Questions
What is a geometric sequence?
A geometric sequence is a list of numbers where each term is multiplied by a fixed ratio called the common ratio (r). For example: 2, 6, 18, 54 has r = 3.
How do you find the nth term of a geometric sequence?
Use the formula aₙ = a₁ × r^(n-1), where a₁ is the first term, r is the common ratio, and n is the term number.
How do you find the common ratio of a geometric sequence?
Divide any term by the previous term. For example, in 4, 12, 36, the common ratio is 12 ÷ 4 = 3.