Question

53, 50, 45, 38, 29, ____

• A. 11
• B. 17
• C. 18
• D. 21

Hint:

When numbers fall quickly but not linearly, try “subtract consecutive odds/evens” or “add consecutive squares/cubes” before more complex rules.

Answer 1

The Correct Option is C

Step 1: Compute first differences
$50-53=-3,\; 45-50=-5,\; 38-45=-7,\; 29-38=-9$.
The sequence is strictly decreasing; the absolute differences are $3,5,7,9$—consecutive odd numbers.
Step 2: Extend the difference pattern
If the rule is “subtract consecutive odd numbers”, the next subtraction is $11$.
Step 3: Find the missing term and verify
$29-11=18$.
Check backward: $18$ would lead to the next term $18-(\text{next odd }13)=5$, which maintains the rule if continued. Hence the pattern is consistent.
Common pitfalls: Mistaking it for an arithmetic progression with constant difference, or for alternating operations. Always list consecutive gaps first.