In the number series 0, 2, 3, 5, 8, 10, 15, 18, 24, 26, 35, one term is wrong. Identify the incorrect term that does not follow the pattern.

Introduction / Context:
The series 0, 2, 3, 5, 8, 10, 15, 18, 24, 26, 35 contains one incorrect term. At first, the differences look messy, but a powerful technique for such questions is to separate the sequence into numbers at odd positions and even positions. Each of those subsequences often follows a neat pattern.

Given Data / Assumptions:

• Series: 0, 2, 3, 5, 8, 10, 15, 18, 24, 26, 35.
• Exactly one term is incorrect.
• We expect the odd indexed and even indexed terms to follow their own patterns.

Concept / Approach:
We label the terms by position and study separately the subsequence of odd position terms (1st, 3rd, 5th, etc.) and even position terms (2nd, 4th, 6th, etc.). If one subsequence shows a clear rule, we then check whether the corresponding values in the original series match that rule, which helps identify the wrong term.

Step-by-Step Solution:
1. Label the positions: 1: 0, 2: 2, 3: 3, 4: 5, 5: 8, 6: 10, 7: 15, 8: 18, 9: 24, 10: 26, 11: 35. 2. Odd position subsequence (1, 3, 5, 7, 9, 11): 0, 3, 8, 15, 24, 35. 3. Compute differences for this subsequence: 3 - 0 = 3, 8 - 3 = 5, 15 - 8 = 7, 24 - 15 = 9, 35 - 24 = 11. 4. The differences are 3, 5, 7, 9, 11 which are consecutive odd numbers. So the odd positions form a perfect pattern. 5. Even position subsequence (2, 4, 6, 8, 10): 2, 5, 10, 18, 26. 6. Compute differences for this subsequence: 5 - 2 = 3, 10 - 5 = 5, 18 - 10 = 8, 26 - 18 = 8. 7. If the even subsequence were to follow the same style, we would expect differences 3, 5, 7, 9. 8. Starting from 2 and adding 3 gives 5; adding 5 gives 10; adding 7 should give 17 (not 18); adding 9 would then give 26. 9. So the correct even subsequence should be 2, 5, 10, 17, 26. 10. That means the term 18 at position 8 is wrong and should be 17 instead.

Verification / Alternative check:
Rebuild the full corrected series: Odd positions: 0, 3, 8, 15, 24, 35 with differences 3, 5, 7, 9, 11. Even positions: 2, 5, 10, 17, 26 with differences 3, 5, 7, 9. Interleave them: 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, 35. Now both subsequences exhibit beautifully increasing odd-number differences.

Why Other Options Are Wrong:

• 8, 24, 35: These sit in the odd position subsequence which already follows the elegant pattern of differences 3, 5, 7, 9, 11. They are correct and should not be changed.

Common Pitfalls:
Many students compute the raw consecutive differences of the full series and find 2, 1, 2, 3, 2, 5, 3, 6, 2, 9, which seems very irregular. Without splitting odd and even positions, it is easy to think the series is random. Systematically examining subsequences is a key skill for these problems.

Final Answer:
The wrong term in the series is 18.