3. The next number in the series 2, 5, 11, 23, 47, ? will be.
A. 95
B. 96
C. 97
D. 98

Pattern Explanation

The series follows a recursive pattern where each term equals the previous term multiplied by 2 plus 1:
a_n+1 = 2 × a_n + 1.

Verify step-by-step:

• 2 × 2 + 1 = 5
• 2 × 5 + 1 = 11
• 2 × 11 + 1 = 23
• 2 × 23 + 1 = 47
• 2 × 47 + 1 = 95

Alternatively, the differences between terms (3, 6, 12, 24) double each time
(next difference 48), so 47 + 48 = 95.

This dual verification confirms consistency across both methods.

Option Analysis

• A. 95: Correct, as 47 × 2 + 1 = 95 or 47 + 48 = 95 matches the established pattern.
• B. 96: Incorrect, arises from 47 × 2 + 2 = 96 (wrong constant) or mistakenly adding 49 instead of 48.
• C. 97: Incorrect, fits neither multiplication (+1 yields 95) nor doubling differences (48 added gives 95).
• D. 98: Incorrect, suggests 47 × 2 + 4 = 98 or an inconsistent difference like 51, breaking the sequence rule.

Exam Insight

The next number series 2, 5, 11, 23, 47 questions test pattern recognition in CSIR NET Life Sciences quantitative aptitude,
emphasizing recursive multiplication by 2 plus 1 or doubling differences for rapid solving.
Practice reinforces distinguishing valid patterns from distractors like 96–98 in competitive exam series.