What number comes next in the sequence: 2, 5, 9, 19, 37, ___?
2011
What number comes next in the sequence: 2, 5, 9, 19, 37, ___?
Answer: C. 75 — ConceptWhen a sequence alternates between two operations, apply the operations in the same repeating order. Here the rule alternates between multiplying by 2…
- A.
76
- B.
74
- C.
75
- D.
50
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept
When a sequence alternates between two operations, apply the operations in the same repeating order. Here the rule alternates between multiplying by 2 and adding 1, then multiplying by 2 and subtracting 1.
Application
Start with 2.
2 × 2 + 1 = 5.
5 × 2 − 1 = 9.
9 × 2 + 1 = 19.
19 × 2 − 1 = 37.
The next operation repeats × 2 + 1, so 37 × 2 + 1 = 75.
Cross-check
Reverse the last operation: (75 − 1) ÷ 2 = 37. Reversing the preceding operation gives (37 + 1) ÷ 2 = 19, which matches the given sequence. Therefore, the next number is 75.