Fill the next term: 10, 14, 26, 42, 70, ? — notice that the “added amounts” follow their own Fibonacci-like sub-sequence.

Introduction / Context:This sequence grows by adding amounts that themselves form a recursive pattern. Recognizing and extending that auxiliary pattern yields the next main term.

Given Data / Assumptions:

• Main series: 10, 14, 26, 42, 70, ?
• Let the added amounts be denoted by d1, d2, d3, …

Concept / Approach:Compute first differences and inspect whether those differences are generated by a secondary recurrence (for example, each difference equals the sum of the previous two). This is common in puzzle sequences.

Step-by-Step Solution:

Verification / Alternative check:The “differences” follow a Fibonacci-like rule starting from 4 and 12. Projecting one more step preserves the structure and gives 114 for the main series.

Why Other Options Are Wrong:

• 100, 102, 106 require differences of 30, 32, or 36 respectively, which do not equal the sum of the previous two differences (16 and 28).

Common Pitfalls:Ignoring that sometimes the differences, not the original terms, carry the key recurrence. Always test the first-difference sequence for structure.

Final Answer:114