Mathematics
Grade 11
15 min
Find terms of a geometric sequence
Find terms of a geometric sequence
What you'll learn
- Identify two or more rectangles that make up a complex shape with 80% accuracy.
- Solve for the area of each individual rectangle within a complex figure and record the answers with correct units (square inches, square feet, etc.) 100% of the time.
- Explain how to find the total area of a complex figure by adding the areas of its individual rectangles in their own words.
- Apply the formula for area (length x width) to find the area of complex figures made of two rectangles, achieving at least 75% accuracy on a worksheet.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a geometric sequence and identify its first term (a₁) and common ratio (r).
Calculate the common ratio of a geometric sequence given any two consecutive terms.
Apply the explicit formula to find any specified term (the nth term) of a geometric sequence.
Determine the first term or common ratio when given two non-consecutive terms in a sequence.
Find a missing term between two non-consecutive terms (a geometric mean).
Solve real-world problems that model geometric growth or decay by finding a specific term.
Ever see a video go viral, jumping from 100 views to 10,000 in just a few shares? 📈 That explosive growth is a perfect example of a geometric sequence at work!
This tutorial will teach you the fundamentals of geometric sequences, which are sequ...
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Key Concepts & Vocabulary
TermDefinitionExample
Geometric SequenceA sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.The sequence 5, 10, 20, 40, ... is a geometric sequence because each term is multiplied by 2 to get the next term.
Term (aₙ)An individual number or element in a sequence. The subscript 'n' denotes the term's position in the sequence.In the sequence 5, 10, 20, 40, ..., the third term is a₃ = 20.
First Term (a₁)The very first number in a sequence.In the sequence 5, 10, 20, 40, ..., the first term is a₁ = 5.
Common Ratio (r)The constant, non-zero number that is multiplied by each term to get the next term. It is found by dividing any term by its preceding term (r = aₙ / aₙ₋₁).In the sequence 5...
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Core Formulas
Common Ratio Formula
r = aₙ / aₙ₋₁
Use this formula to find the common ratio (r). Simply divide any term in the sequence by the term that comes immediately before it. This should be constant for the entire sequence.
Explicit Formula for the nth Term
aₙ = a₁ * r^(n-1)
This is the most important formula for finding terms. Use it to calculate the value of any term (aₙ) when you know the first term (a₁), the common ratio (r), and the position of the term you want to find (n).
4 more steps in this tutorial
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Challenging
The first three terms of a geometric sequence are x-2, x+1, and x+7. Find the value of x.
A.5
B.-1/3
C.3
D.-4
Challenging
In a geometric sequence, a₃ = 18 and a₅ = 162. What is a possible value for the 2nd term (a₂)?
A.54
B.6
C.9
D.2
Challenging
A scientist observes a mold culture that covers 100 mm². The area covered increases by 30% every 6 hours. What is the approximate area covered at the end of a full day (24 hours)?
A.219.7 mm²
B.169.0 mm²
C.285.6 mm²
D.130.0 mm²
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Frequently asked questions
What grade level is "Find terms of a geometric sequence"?
Find terms of a geometric sequence is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Find terms of a geometric sequence?
You'll be able to: Identify two or more rectangles that make up a complex shape with 80% accuracy; Solve for the area of each individual rectangle within a complex figure and record the answers with correct units (square inches, square feet, etc.)….
Is "Find terms of a geometric sequence" free to practice?
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How many practice questions are included with Find terms of a geometric sequence?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.