What is a Sequence of Multiples?

S1-SA5-0215

Grade Level:

Class 4

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

A sequence of multiples is a list of numbers that are all multiples of the same number, arranged in increasing order. It starts with the number itself and then lists all the numbers you get by multiplying it by 2, then 3, then 4, and so on.

Simple Example

Quick Example

Imagine you are buying ladoos for a party. If one ladoo costs 10 rupees, then 2 ladoos cost 20 rupees, 3 ladoos cost 30 rupees, and so on. The cost of the ladoos (10, 20, 30, 40, ...) forms a sequence of multiples of 10.

Worked Example

Step-by-Step

Let's find the first 5 multiples of 7.

STEP 1: Start with the number itself, which is 7.

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STEP 2: Multiply 7 by 2. 7 x 2 = 14.

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STEP 3: Multiply 7 by 3. 7 x 3 = 21.

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STEP 4: Multiply 7 by 4. 7 x 4 = 28.

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STEP 5: Multiply 7 by 5. 7 x 5 = 35.

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ANSWER: The first 5 multiples of 7 are 7, 14, 21, 28, 35.

Why It Matters

Understanding sequences of multiples helps you see patterns in numbers, which is crucial for higher math like algebra and geometry. Engineers use this concept to design repeating structures, and computer programmers use it in coding to create repeating actions or schedules.

Common Mistakes

MISTAKE: Forgetting to include the number itself as the first multiple. For example, listing 6, 9, 12 as multiples of 3. | CORRECTION: Always start with the number itself. The multiples of 3 are 3, 6, 9, 12, and so on.

MISTAKE: Confusing multiples with factors. For example, saying 2 is a multiple of 4. | CORRECTION: Multiples are numbers you get by multiplying. Factors are numbers that divide evenly into another number. 4 is a multiple of 2 (2 x 2 = 4), but 2 is a factor of 4.

MISTAKE: Listing numbers that are not exact products. For example, saying 10, 20, 25, 30 are multiples of 5. | CORRECTION: Every number in the sequence must be an exact product of the original number and a counting number (1, 2, 3...). 25 is a multiple of 5, but 20 is also a multiple of 5. The sequence should be 5, 10, 15, 20, 25, 30.

Practice Questions

Try It Yourself

QUESTION: Write the first 4 multiples of 6. | ANSWER: 6, 12, 18, 24

QUESTION: Which of these numbers is NOT a multiple of 8: 16, 24, 30, 40? | ANSWER: 30

QUESTION: An auto-rickshaw charges 5 rupees for every kilometer. If you travel 1 km, 2 km, 3 km, 4 km, and 5 km, what is the sequence of charges you will pay? | ANSWER: 5, 10, 15, 20, 25 rupees

MCQ

Quick Quiz

Which of the following is a sequence of multiples of 9?

9, 18, 27, 35

9, 18, 27, 36

1, 9, 18, 27

9, 19, 29, 39

The Correct Answer Is:

Option B correctly lists numbers that are 9 x 1, 9 x 2, 9 x 3, and 9 x 4. Options A, C, and D contain numbers that are not exact multiples of 9.

Real World Connection

In the Real World

Sequences of multiples are used in planning and scheduling. For example, a bus service might have buses arriving at a stop every 15 minutes. The arrival times (if starting at 0 minutes) would be 0, 15, 30, 45 minutes, forming a sequence of multiples of 15. This helps commuters in cities like Mumbai or Delhi plan their journeys.

Key Vocabulary

Key Terms

MULTIPLE: The result of multiplying a number by another whole number. | SEQUENCE: An ordered list of numbers. | PRODUCT: The result of multiplication. | COUNTING NUMBERS: The numbers 1, 2, 3, 4, and so on.

What's Next

What to Learn Next

Now that you understand sequences of multiples, you can explore 'Least Common Multiple (LCM)'. LCM helps you find the smallest number that is a multiple of two or more different numbers, which is very useful for adding fractions!