A number series is given with one term missing. Study the pattern in 0, 3, 8, ?, 24, 35 and choose the correct alternative that will complete the series.

Introduction / Context:
This problem is a classic number series question where one middle term is missing. The given series is 0, 3, 8, ?, 24, 35. The aim is to identify the pattern that generates each term and then use it to find the missing value. Such questions assess the candidate's numerical reasoning skills and familiarity with common series types such as squares, cubes, and other polynomial patterns.

Given Data / Assumptions:
Given series: 0, 3, 8, ?, 24, 35.
Exactly one term is missing between 8 and 24.
We assume that the same rule is used consistently for all terms.
The correct answer must be one of the provided options and must fit the pattern perfectly.

Concept / Approach:
A useful approach with small, steadily increasing series is to check whether terms relate to perfect squares or cubes with a fixed adjustment. Observing the numbers, we notice that they can be expressed as n^2 minus 1 for consecutive values of n. That is, 1^2 minus 1, 2^2 minus 1, 3^2 minus 1, and so on. This suggests a simple formula-driven pattern rather than a random difference pattern.

Step-by-Step Solution:
For n = 1: 1^2 - 1 = 1 - 1 = 0 (first term). For n = 2: 2^2 - 1 = 4 - 1 = 3 (second term). For n = 3: 3^2 - 1 = 9 - 1 = 8 (third term). For n = 4: 4^2 - 1 = 16 - 1 = 15 (this must be the missing term). For n = 5: 5^2 - 1 = 25 - 1 = 24 (matches the given fifth term). For n = 6: 6^2 - 1 = 36 - 1 = 35 (matches the last term). Thus, the missing number is 15.

Verification / Alternative check:
We verify the pattern across all known positions. Each term fits the formula term = n^2 - 1 for n = 1 to 6. The given numbers at positions 1, 2, 3, 5, and 6 all align exactly with the formula. The only value that makes the fourth term consistent is 15, since 4^2 - 1 equals 15. Therefore the pattern is robust and uniquely determines the missing value.

Why Other Options Are Wrong:
Option B: 16 would correspond to 4^2, not 4^2 - 1, and would break the consistent use of minus 1.
Option C: 18 does not fit any simple square minus 1 sequence for the positions in this series.
Option D: 9 would be equal to 3^2, which already appears in adjusted form at position three, so it is inconsistent here.
Option E: 21 also does not correspond to n^2 - 1 for any integer n between 1 and 6 in this context.

Common Pitfalls:
Many students focus only on differences between terms (3, 5, ?, ?, 11) and do not realise that the series comes from squares. Differences alone look irregular and may lead to guessing. Another common mistake is to check cubes or mixed patterns before testing the simplest possible square-based pattern. Remember that exam questions frequently use small adjustments such as plus or minus 1 applied to basic powers of integers.

Final Answer:
The only value that maintains the pattern n^2 minus 1 is 15, so the correct option is 15.