Number series – find the next term. Sequence: 10, 5, 13, 10, 16, 20, 19, ( ? )
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A22
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B40
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C38
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D23
Answer
Correct Answer: 40
Explanation
Introduction / Context:Many number series interleave two independent subsequences at odd and even positions. Isolating each subsequence often reveals simple patterns that make the next term obvious.
Given Data / Assumptions:
- Overall sequence: 10, 5, 13, 10, 16, 20, 19, ( ? )
- We expect two interleaved patterns: one for odd positions, one for even positions.
Concept / Approach:Separate odd-indexed terms and even-indexed terms and analyze each independently. Common rules include constant increments for one and doubling or halving for the other.
Step-by-Step Solution:
Odd positions (1st, 3rd, 5th, 7th): 10, 13, 16, 19 – this is +3 each time.Even positions (2nd, 4th, 6th): 5, 10, 20 – this is times 2 each step.The next term is the 8th term (even position), so apply the even-position rule: 20 * 2 = 40.Verification / Alternative check:Project forward: if a 9th term were needed (odd position), it would be 19 + 3 = 22, which is consistent, reinforcing the correctness of the extracted rules.
Why Other Options Are Wrong:
- 22: That would be correct for the next odd position, not the 8th term.
- 38 and 23: Do not follow either identified rule from the immediately prior relevant subsequence term.
Common Pitfalls:Trying to force a single-step rule on the entire sequence rather than splitting into interleaved streams.
Final Answer:40