Mathematics
Grade 4
15 min
Write variable expressions for geometric sequences
Write variable expressions for geometric sequences
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1
Introduction & Learning Objectives
Learning Objectives
Identify a geometric sequence within a set of measurements.
Determine the common ratio (the multiplier) in a simple geometric sequence.
Understand that a variable, like 'n', can represent the value of any term in a sequence.
Write a simple variable expression to find the next term in a geometric sequence involving units of measurement.
Use a variable expression to calculate the next term in a sequence.
Describe the multiplicative relationship between terms in a geometric sequence.
Imagine a magical seed that grows into a plant that doubles its height in centimeters every single day! 🌱 How could we create a math rule to predict its height tomorrow?
In this lesson, you will become a pattern detective! We will learn about special patterns called...
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Key Concepts & Vocabulary
TermDefinitionExample
SequenceA list of numbers or measurements that follow a specific rule or order.2 cm, 4 cm, 6 cm, 8 cm... is a sequence.
TermEach number or measurement in a sequence.In the sequence 5, 10, 20, 40, the number 20 is the third term.
Geometric SequenceA sequence where you multiply by the exact same number each time to get the next term.1 gram, 3 grams, 9 grams, 27 grams... (you multiply by 3 each time).
Common RatioThe number you multiply by to get from one term to the next in a geometric sequence.In the sequence 2, 4, 8, 16, the common ratio is 2.
VariableA letter (like n, x, or c) that takes the place of a number that can change.In the math phrase c * 4, 'c' is the variable.
Variable ExpressionA math phrase with numbers, variables, and operation signs. It does...
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Core Formulas
The 'Next Term' Rule
Next Term = Current Term * r
To find any term in a geometric sequence, take the term right before it (the current term) and multiply it by the common ratio, which we call 'r'.
The Variable Expression Rule
Let 'n' be the current term. The expression for the next term is n * r.
We can use a variable like 'n' to stand for any term's value. To write a rule for the next term, we write an expression showing 'n' being multiplied by the common ratio 'r'.
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Challenging
A baker makes a giant 64-ounce loaf of bread. Each day, a family eats half of the loaf that is remaining. What variable expression (using 'b' for the current amount of bread) describes this, and how many ounces are left at the start of Day 4?
A.Expression: b * 2; Amount: 256 ounces
B.Expression: b * (1/2); Amount: 16 ounces
C.Expression: b - 32; Amount: 0 ounces
D.Expression: b * (1/2); Amount: 8 ounces
Challenging
The variable expression for a shrinking ice sculpture's volume is `v * (1/3)`. The fourth measurement taken was 10 cubic meters. What was the third measurement?
A.30 cubic meters
B.3.33 cubic meters
C.90 cubic meters
D.40 cubic meters
Challenging
A video game character's power level starts at 100 points. With a special gem, its power increases by half of its current value every minute. The sequence is 100, 150, 225, ... What is the common ratio?
A.1/2
B.2
C.1.5
D.50
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