Number series — continue the Fibonacci-like pattern. Sequence: 5, 2, 7, 9, 16, 25, ?

Introduction / Context:
This is a sum-of-previous-two sequence (a Fibonacci-style recurrence) but started with custom seed values. Many exam sets include such recurrences where each term equals the sum of the two immediately preceding terms.

Given Data / Assumptions:

• Sequence given: 5, 2, 7, 9, 16, 25, ?
• We test the recurrence a(n) = a(n−1) + a(n−2).

Concept / Approach:
Verify the rule across each step: 5 + 2 = 7, 2 + 7 = 9, 7 + 9 = 16, 9 + 16 = 25. If consistent, compute the next as 16 + 25.

Step-by-Step Solution:
Check term 3: 5 + 2 = 7 (fits). Term 4: 2 + 7 = 9 (fits). Term 5: 7 + 9 = 16 (fits). Term 6: 9 + 16 = 25 (fits). Next term: 16 + 25 = 41.

Verification / Alternative check:
Continue one more step mentally: after 41, the next would be 25 + 41 = 66, reinforcing that the rule holds.

Why Other Options Are Wrong:
45/48/52: None equals 16 + 25; they violate the “sum of last two” rule.

Common Pitfalls:
Looking for multiplicative patterns or alternating sequences, when a simple two-term sum explains all transitions.

Final Answer:
41