Problem
Find the pattern and next two terms: 3, 7, 11, 15, 19, ...
📝Step-by-Step Solution
1
Find differences between terms
7-3=4, 11-7=4, 15-11=4, 19-15=4. The difference is constant!
Common difference = 4
2
Identify the sequence type
Since the difference between consecutive terms is constant (4), this is an arithmetic sequence.
3
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
4
Find the next term
19 + 4 = 23
6th term = 23
5
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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