Complete the series by identifying the pattern in successive differences: 6, 9, 15, 27, 51, ?

Introduction / Context:Some series grow by differences that double every step. Recognizing this yields the next term quickly.

Given Data / Assumptions:

• Series: 6, 9, 15, 27, 51, ?
• Expect a simple deterministic pattern in first differences.

Concept / Approach:Compute consecutive differences: 9−6, 15−9, 27−15, 51−27, … and see if they follow a doubling law.

Step-by-Step Solution:

Verification / Alternative check:Working backward: 99 − 51 = 48, neatly continuing the doubling sequence.

Why Other Options Are Wrong:84, 123, 75 would require breaking the clean doubling of the differences.

Common Pitfalls:Mistaking the series for geometric progression; it is an arithmetic progression of differences.

Final Answer:99.