Find the missing number: 56, 58, 62, ?, 86, 118, 182

The correct answer is (B) 74.

• Given Series and Principle: The given number series is 56, 58, 62, ?, 86, 118, 182. To find the missing number, we need to analyze the difference between consecutive terms to identify the underlying pattern.
• Step-by-Step Calculation: Let us find the differences between adjacent terms: 58 - 56 = 2, 62 - 58 = 4. Notice that the differences are powers of 2 (2^1 = 2, 2^2 = 4). Following this geometric progression, the next difference should be 2^3 = 8. Adding 8 to the third term: 62 + 8 = 70. Let us verify the subsequent differences: 2^4 = 16, so 70 + 16 = 86 (matches the fifth term); 2^5 = 32, so 86 + 32 = 118 (matches the sixth term); 2^6 = 64, so 118 + 64 = 182 (matches the seventh term). Thus, the missing number is 70? Wait, let us check: 56 + 2 = 58; 58 + 4 = 62; 62 + 8 = 70. Therefore, 70 is the correct missing number, which corresponds to option (D). Correction: Option index is (D) 70. Let us re-verify: Option (B) is 74, Option (D) is 70. The calculated missing number is 70.
• Verification and Option Contrast: The differences follow the sequence 2, 4, 8, 16, 32, 64. Hence, 62 + 8 = 70 makes the series consistent. Options (A), (B), and (C) fail to satisfy the geometric difference pattern.