Question:
2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, ?
2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, ?
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When working with sequences, check for missing terms and identify the exclusion pattern before guessing the next term.
Updated On: Aug 12, 2025
- 22
- 23
- 24
- 25
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The Correct Option is B
Solution and Explanation
Step 1: First, observe the sequence. It contains most numbers starting from 2, but clearly some are skipped.
Step 2: Look closely — numbers missing are 5, 10, and 16. These missing numbers are those that are multiples of 5 or of the form \( n^2 + 1 \) (e.g., 16).
Step 3: The given sequence is almost consecutive natural numbers except the ones which are composite multiples of 5 or certain squares are omitted.
Step 4: After 21, the next number in counting order is 22, which is present in natural order, but here the sequence logic removes no number between 21 and 23.
Step 5: Check: 22 is even and has no exclusion in the logic, so next number is 23, which is also prime.
Step 6: Since we’re to find the very next term after 21 in this sequence, it is 23.
Step 7: Elimination: - Option (a) 22 — would fit natural counting but is excluded by the pattern here.
- Option (c) 24 — comes after 23, so too far.
- Option (d) 25 — excluded since it's a multiple of 5.
Step 2: Look closely — numbers missing are 5, 10, and 16. These missing numbers are those that are multiples of 5 or of the form \( n^2 + 1 \) (e.g., 16).
Step 3: The given sequence is almost consecutive natural numbers except the ones which are composite multiples of 5 or certain squares are omitted.
Step 4: After 21, the next number in counting order is 22, which is present in natural order, but here the sequence logic removes no number between 21 and 23.
Step 5: Check: 22 is even and has no exclusion in the logic, so next number is 23, which is also prime.
Step 6: Since we’re to find the very next term after 21 in this sequence, it is 23.
Step 7: Elimination: - Option (a) 22 — would fit natural counting but is excluded by the pattern here.
- Option (c) 24 — comes after 23, so too far.
- Option (d) 25 — excluded since it's a multiple of 5.
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