What is What Comes Next in a Sequence?

S0-SA3-0407

Grade Level:

Pre-School – Class 2

All domains without exception

Definition

What is it?

Finding 'what comes next' in a sequence means figuring out the pattern or rule that connects the numbers or items in a list and then applying that rule to find the next item. It's like predicting the next step based on the steps you've already seen.

Simple Example

Quick Example

Imagine your cricket team scores runs like this in five overs: 5, 10, 15, 20, 25. What comes next? You can see that 5 runs are added each time. So, after 25, the next score would be 30.

Worked Example

Step-by-Step

Let's find what comes next in the sequence: 2, 4, 6, 8, __.

1. Look at the first two numbers: 2 and 4. What's the difference? 4 - 2 = 2.
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2. Look at the next pair: 4 and 6. What's the difference? 6 - 4 = 2.
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3. Look at the next pair: 6 and 8. What's the difference? 8 - 6 = 2.
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4. It looks like the pattern is 'add 2' to the previous number.
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5. To find the next number, add 2 to the last number in the sequence, which is 8.
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6. 8 + 2 = 10.

ANSWER: The next number in the sequence is 10.

Why It Matters

Understanding sequences helps you develop logical thinking and problem-solving skills, which are super useful in many subjects. It's crucial in fields like data science for predicting trends, in finance for forecasting market changes, and even in computer programming for creating algorithms.

Common Mistakes

MISTAKE: Only checking the first two numbers for a pattern and assuming it continues. | CORRECTION: Always check at least three or four numbers to confirm the pattern before making a prediction. Some patterns change or are more complex.

MISTAKE: Confusing addition/subtraction patterns with multiplication/division patterns. | CORRECTION: Try different operations (add, subtract, multiply, divide) to see which one fits the sequence best. Don't stick to just one type of operation.

MISTAKE: Not considering 'skipping' patterns (e.g., adding 2, then adding 3, then adding 4). | CORRECTION: If a simple pattern doesn't emerge, look for patterns in the *differences* between numbers, or look for alternating patterns.

Practice Questions

Try It Yourself

QUESTION: What comes next in the sequence: 10, 20, 30, 40, __? | ANSWER: 50

QUESTION: Find the next number: 3, 6, 12, 24, __? | ANSWER: 48

QUESTION: What is the next term in the series: 1, 4, 9, 16, __? (Hint: Think about squares!) | ANSWER: 25

MCQ

Quick Quiz

What is the next number in the sequence: 100, 95, 90, 85, __?

The Correct Answer Is:

The pattern is to subtract 5 from the previous number. 85 - 5 = 80. Options B, C, and D do not follow this pattern.

Real World Connection

In the Real World

Many apps you use daily rely on understanding sequences. For example, when a food delivery app like Swiggy predicts how long your order will take, it uses patterns from past delivery times. Even ISRO scientists use complex sequences to predict satellite orbits!

Key Vocabulary

Key Terms

SEQUENCE: An ordered list of numbers or objects following a specific rule | PATTERN: The rule or design that repeats or progresses in a sequence | TERM: Each individual number or object in a sequence | PREDICTION: Using the pattern to guess what comes next

What's Next

What to Learn Next

Now that you understand basic sequences, you can explore different types like arithmetic progressions (where you add/subtract the same number) and geometric progressions (where you multiply/divide by the same number). Keep practicing to become a sequence master!