Question

In the following question, select the missing number from the given series.
2, 5, 17, 71, ?

• A. 349
• B. 359
• C. 369
• D. 379

Hint:

For number series where the difference between terms grows exponentially, always test for patterns involving both multiplication and addition/subtraction, like \( (x \times n) \pm m \).

Answer 1

The Correct Option is B

Step 1: Analyze the relationship between consecutive numbers in the series. The series increases rapidly, which suggests multiplication is involved. - From 2 to 5: \( 2 \times 2 + 1 = 5 \) - From 5 to 17: \( 5 \times 3 + 2 = 17 \) - From 17 to 71: \( 17 \times 4 + 3 = 68 + 3 = 71 \)
Step 2: Identify the underlying pattern. The pattern is: \( \text{Next Term} = (\text{Previous Term} \times n) + (n-1) \), where 'n' starts at 2 and increases by 1 for each step.
Step 3: Apply the pattern to find the missing number. The next step in the pattern will use n=5. Missing Number = \( (71 \times 5) + (5-1) \) Missing Number = \( 355 + 4 = 359 \).