Question:

20, 30, 42, 56, 72, ____

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If first differences form their own simple AP, extend that AP rather than guessing the next term directly.
Updated On: Aug 14, 2025
  • 82
  • 90
  • 92
  • 94
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The Correct Option is B

Solution and Explanation

Step 1: Compute differences
$30-20=10,\; 42-30=12,\; 56-42=14,\; 72-56=16$.
The increments are $10,12,14,16$—an arithmetic progression with common difference $2$.
Step 2: Extend the AP of differences
Next increment $=16+2=18$.
Step 3: Add to the last term
$72+18=90$.
Verification: If we continued, the next would be $90+20=110$, preserving the pattern $10,12,14,16,18,20,\dots$
Why other options fail:
$82, 92, 94$ break the “+2 to each gap” rule at some point; only $90$ keeps the uniform step growth.
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