The first 5 terms of a number pattern are: 2, 5, 11, 23, 47. What is the 6th term?
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Worked Solution
Step 1: Find the differences between consecutive terms.
5 − 2 = 3
11 − 5 = 6
23 − 11 = 12
47 − 23 = 24
The differences are 3, 6, 12, 24 — each difference doubles.
Step 2: Find the next difference.
Next difference = 24 × 2 = 48
Step 3: Find the 6th term.
6th term = 47 + 48 = 95
Answer: The 6th term is 95.
Alternative rule: Each term = previous term × 2 + 1.
Check: 2×2+1=5 ✓, 2×5+1=11 ✓, 2×11+1=23 ✓, 2×23+1=47 ✓
6th term = 47×2+1 = 95 ✓
Correct answer: 95
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