Medium📚 Number Sequences

Number Sequence Example

Grades 7-8Key Stage 3Årskurs 7-8

Problem

Find the pattern and next two terms: 3, 7, 11, 15, 19, ...

📝Step-by-Step Solution

Find differences between terms

7-3=4, 11-7=4, 15-11=4, 19-15=4. The difference is constant!

Common difference = 4

Identify the sequence type

Since the difference between consecutive terms is constant (4), this is an arithmetic sequence.

Write the rule

Each term = previous term + 4. Or: nth term = first term + (n-1) × difference = 3 + (n-1) × 4 = 4n - 1

aₙ = 4n - 1

Find the next term

19 + 4 = 23

6th term = 23

Find one more term

23 + 4 = 27

7th term = 27

✅Final Answer

Next two terms: 23, 27

This arithmetic sequence adds 4 each time. The formula aₙ = 4n - 1 lets you find any term directly: a₁₀ = 4(10) - 1 = 39. For geometric sequences, you'd multiply by a constant ratio instead of adding.

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