In the series 12, 24, 26.5, 79.5, ?, 330, what number should replace the question mark to complete the pattern?

Introduction / Context:
This number series mixes multiplication and addition in an alternating way. The multipliers and addends are changing, but in a controlled pattern. Being able to detect such alternating operations is very useful in medium difficulty series questions in aptitude exams.

Given Data / Assumptions:

• Series: 12, 24, 26.5, 79.5, ?, 330.
• Exactly one missing term is to be found.
• The pattern likely alternates between multiplication and addition.

Concept / Approach:
We first compare consecutive terms to see whether there is multiplication or addition. The jump from 12 to 24 suggests multiplication by 2. The jump from 24 to 26.5 is a small increase, more likely addition. From 26.5 to 79.5 is a larger increase that fits multiplication by 3. This strongly suggests a pattern: multiply by a number, then add a related number, then multiply by the next number, and so on.

Step-by-Step Solution:
From 12 to 24: 12 * 2 = 24. So the first operation is multiplication by 2.From 24 to 26.5: 24 + 2.5 = 26.5. So the next operation is addition of 2.5.From 26.5 to 79.5: 26.5 * 3 = 79.5. So now we multiply by 3.This suggests a pattern: multiply by 2, add 2.5, multiply by 3, add 3, multiply by 4, add 4.5 and so on.From 79.5 to the missing term, we should add 3. So the missing term is 79.5 + 3 = 82.5.From 82.5 to 330, we check the next operation: 82.5 * 4 = 330, which fits perfectly.

Verification / Alternative check:
The full operations are therefore: 12 * 2 = 24, 24 + 2.5 = 26.5, 26.5 * 3 = 79.5, 79.5 + 3 = 82.5, 82.5 * 4 = 330. The multipliers increase as 2, 3 and 4 and the added numbers increase from 2.5 to 3 in a simple manner. This creates a clear, consistent pattern that uniquely picks 82.5 as the missing term. No other option gives a smooth alternation of multiplication and addition that matches the given numbers.

Why Other Options Are Wrong:
211, 101.5, 99 and 90.5 do not satisfy the rule that from that term, multiplying by 4 gives exactly 330. They either break the add 3 step from 79.5 or do not allow a clean multiplication by 4 to reach 330. Any choice other than 82.5 forces an inconsistent or forced pattern.

Common Pitfalls:
Students sometimes try only constant multiplication or constant addition, both of which fail here. Others may misread 26.5 and 79.5 and not notice that 26.5 * 3 equals 79.5 exactly. The key idea is to suspect alternating operations when consecutive jumps change size drastically and then verify that by performing the calculations carefully.

Final Answer:
The missing term in the series is 82.5.