Number series – find the next term: 1, 5, 13, 25, 41, ? Observe the first differences (+4, +8, +12, +16). Continue the pattern to determine the missing term.
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A63
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B57
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C61
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D51
Answer
Correct Answer: 61
Explanation
Introduction / Context:Many number-series items are built from regular first differences. When those first differences themselves rise by a fixed amount, the series is quadratic-like with constant second difference. Spotting that constant increment unlocks the answer quickly.
Given Data / Assumptions:
- Series: 1, 5, 13, 25, 41, ?
- We assume a clean deterministic rule continues.
Concept / Approach:Compute first differences and then check if those differences progress in a simple pattern (e.g., constant increment). If first differences increase by a constant k, then the next first difference is the previous one plus k.
Step-by-Step Solution:
First differences: 5−1=4, 13−5=8, 25−13=12, 41−25=16.These rise by +4 each time (4, 8, 12, 16 → next should be 20).Add the next difference to the last term: 41 + 20 = 61.Verification / Alternative check:If second difference is constant (+4), extending by +20 is consistent and yields a smoothly growing sequence without anomalies.
Why Other Options Are Wrong:
51, 57, 63 do not maintain the +4 step in the differences (their back-calculated first differences would break the +4 pattern).Common Pitfalls:Jumping to multiplicative rules or cubes prematurely. Always try first- and second-difference checks first.
Final Answer:61