Question Bank • QB_EXP_GA_SER_003
NAT • 2 Marks
Section 8: General Aptitude
Analytical: Number Series, Letter Patterns & Codes
Subtopic: Difference of differences series pattern
Question Statement:
Identify the next number in the arithmetic series: $3, \; 7, \; 15, \; 31, \; 63$, ________.
Step-by-Step Solution & Explanation
Pattern: each term is $T_{n+1} = 2 T_n + 1$ (or $T_n = 2^{n+1} - 1$):
- $2(3) + 1 = 7$
- $2(7) + 1 = 15$
- $2(15) + 1 = 31$
- $2(31) + 1 = 63$
- Next term $= 2(63) + 1 = 126 + 1 = 127$.
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