Question

What should come in place of the question mark (?) in the given series?

4 6 10 18 34 ?

• A. 67
• B. 65
• C. 68
• D. 66

Answer 1

Answer:

D. 66

Number Series Analysis: 4, 6, 10, 18, 34, ?

Understanding the Pattern

• Observe the differences between consecutive terms:
• 6 - 4 = 2
• 10 - 6 = 4
• 18 - 10 = 8
• 34 - 18 = 16
• The differences themselves form a series: 2, 4, 8, 16. This is a geometric progression where each term is double the previous term (powers of 2: 2¹, 2², 2³, 2⁴).

Determining the Next Term

• Following the pattern of differences, the next difference should be 16 * 2 = 32.
• Add this difference to the last term of the original series: 34 + 32 = 66.

Alternative Pattern (Doubling the previous difference and adding to the current term)

• Starting with 4:
• 4 + (2 * 1) = 6
• 6 + (2 * 2) = 10
• 10 + (2 * 4) = 18
• 18 + (2 * 8) = 34
• 34 + (2 * 16) = 66

Conclusion

The number that should come in place of the question mark is 66.