Geometric Sequence
Geometric Sequence is a Grade 8 algebra topic in Saxon Math Course 3, Chapter 7, where each term is found by multiplying the previous term by a constant ratio. Students learn to identify geometric sequences, find the constant ratio by dividing consecutive terms, and calculate future terms. This concept underpins exponential growth patterns essential for algebra and beyond.
Key Concepts
Property A geometric sequence has a constant ratio between terms. To find it, divide any term by the one that precedes it: $\frac{9}{3}=3$, $\frac{27}{9}=3$.
Examples In the sequence $2, 6, 18, 54, \dots$, the constant ratio is $\frac{6}{2}=3$. For the sequence $100, 50, 25, \dots$, the constant ratio is $\frac{1}{2}$. The next term is $12.5$. To find the next term of $4, 16, 64, \dots$, you multiply by the ratio 4: $64 \times 4 = 256$.
Explanation This sequence is all about multiplication! Each term is found by multiplying the previous one by a fixed number, the 'constant ratio.' This makes the sequence grow incredibly fast, like a viral video. When you graph these sequences, they don't make a straight line but a cool curve that shoots upward, showing that explosive, geometric growth.
Common Questions
What is a geometric sequence in Grade 8 math?
A geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by the same fixed number, called the constant ratio. For example, 2, 6, 18, 54 is a geometric sequence with a constant ratio of 3.
How do you find the constant ratio of a geometric sequence?
Divide any term by the term immediately before it. If the result is the same for every consecutive pair, that number is the constant ratio.
How is a geometric sequence different from an arithmetic sequence?
In an arithmetic sequence you add or subtract a fixed number each time, while in a geometric sequence you multiply or divide by a fixed number each time.
What textbook covers geometric sequences in Grade 8?
Geometric sequences are covered in Saxon Math Course 3, Chapter 7: Algebra, which is used in many Grade 8 classrooms.
How do you find the next term in a geometric sequence?
Multiply the last known term by the constant ratio. For example, in the sequence 4, 20, 100, 500, the constant ratio is 5, so the next term is 500 × 5 = 2500.