Number series – compute the next term using a “difference ×3 + 2” rule: 8, 10, 18, 44, 124, ? First differences follow d_{n} = d_{n-1} * 3 + 2.

Introduction / Context:Some non-linear series are governed by a recurrence on the differences, not the terms. Recognizing and extending that difference-recurrence gives the next value directly.

Given Data / Assumptions:

• Terms: 8, 10, 18, 44, 124, ?
• First differences: 2, 8, 26, 80, …

Concept / Approach:Model the first differences. Test d2=2*3+2=8; d3=8*3+2=26; d4=26*3+2=80. The fit is exact, so extend once more using the same rule.

Step-by-Step Solution:

Verification / Alternative check:Back-substitute differences to reconstruct all terms; the recurrence holds at each step.

Why Other Options Are Wrong:

Common Pitfalls:Trying multiplicative ratios on the terms; here the hidden structure is in the differences.

Final Answer:366