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What is a Sequence of Numbers that Double?
Grade Level:
Class 5
All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry
Definition
What is it?
A sequence of numbers that double is a list where each number after the first one is found by multiplying the previous number by 2. It's like a chain reaction where numbers keep growing bigger and bigger, always by multiplying by two.
Simple Example
Quick Example
Imagine you have 1 samosa. Your friend gives you double that, so you have 2 samosas. Then another friend doubles that, so you have 4 samosas. The sequence of samosas is 1, 2, 4. Each number is double the one before it.
Worked Example
Step-by-Step
Let's find the next three numbers in the sequence: 3, 6, 12, ...
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Step 1: Understand the rule. The problem says 'numbers that double', so each number is twice the previous one.
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Step 2: Find the second number. It is 3 x 2 = 6. This matches the sequence given.
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Step 3: Find the third number. It is 6 x 2 = 12. This also matches the sequence given.
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Step 4: Find the fourth number. Multiply the third number (12) by 2. So, 12 x 2 = 24.
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Step 5: Find the fifth number. Multiply the fourth number (24) by 2. So, 24 x 2 = 48.
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Step 6: Find the sixth number. Multiply the fifth number (48) by 2. So, 48 x 2 = 96.
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Answer: The next three numbers in the sequence are 24, 48, 96.
Why It Matters
Understanding doubling sequences helps us see how things grow very fast, like money in a bank or how a small virus can spread. This idea is used by scientists to predict populations, by computer programmers to make games, and even in finance to calculate investments.
Common Mistakes
MISTAKE: Adding 2 instead of multiplying by 2. For example, seeing 2, 4, 6, 8... and thinking it's a doubling sequence. | CORRECTION: Always multiply the previous number by 2. A doubling sequence would be 2, 4, 8, 16...
MISTAKE: Forgetting the first number and starting the doubling from 0 or 1 always. | CORRECTION: The first number is given or assumed. You start doubling from that specific first number, whatever it is.
MISTAKE: Calculating incorrectly when numbers get large, especially with mental math. For example, 24 x 2 = 46. | CORRECTION: Double-check your multiplication, especially for larger numbers. If needed, write down the multiplication steps.
Practice Questions
Try It Yourself
QUESTION: What is the next number in the sequence: 5, 10, 20, __? | ANSWER: 40
QUESTION: A small plant doubles its height every week. If it is 6 cm tall this week, how tall will it be in 3 weeks? | ANSWER: Week 1: 6 cm, Week 2: 12 cm, Week 3: 24 cm. So, 24 cm.
QUESTION: Starting with 2 rupees, if your money doubles every day, how much money will you have after 5 days? | ANSWER: Day 1: 2, Day 2: 4, Day 3: 8, Day 4: 16, Day 5: 32. So, 32 rupees.
MCQ
Quick Quiz
Which of these is a sequence where numbers double?
1, 3, 5, 7
2, 4, 6, 8
3, 6, 12, 24
5, 10, 15, 20
The Correct Answer Is:
C
Option C (3, 6, 12, 24) is correct because each number is found by multiplying the previous number by 2. Options A, B, and D show sequences that add a constant number, not multiply by 2.
Real World Connection
In the Real World
You see doubling in real life when a bank offers 'double interest' on your savings, or when mobile data plans offer to 'double your data' for a special price. Even how quickly news spreads on WhatsApp or Instagram can sometimes feel like a doubling sequence, starting from one person sharing!
Key Vocabulary
Key Terms
SEQUENCE: An ordered list of numbers following a rule | DOUBLE: To multiply by 2 | PREVIOUS NUMBER: The number that comes just before the current one | MULTIPLY: To find the product of numbers
What's Next
What to Learn Next
Now that you understand doubling sequences, you can explore other types of number patterns like sequences that triple, or sequences that add a constant number. These ideas are building blocks for understanding more complex math concepts like geometric progressions.
