Understanding the Number Series Pattern

The question asks us to identify the pattern in the given number series and find the missing term represented by the question mark (?). The series provided is: $12, 6, 6, 9, 18, ?$.

Analyzing the Series Progression

Let's examine the relationship between consecutive terms in the series:

• From the first term ($12$) to the second term ($6$): $12 \div 2 = 6$, or $12 \times 0.5 = 6$.
• From the second term ($6$) to the third term ($6$): $6 \times 1 = 6$.
• From the third term ($6$) to the fourth term ($9$): $6 \times 1.5 = 9$.
• From the fourth term ($9$) to the fifth term ($18$): $9 \times 2 = 18$.

Identifying the Pattern in Operations

Observe the multipliers used to get from one term to the next:

• Multiplier 1: $0.5$
• Multiplier 2: $1.0$
• Multiplier 3: $1.5$
• Multiplier 4: $2.0$

This sequence of multipliers ($0.5, 1.0, 1.5, 2.0$) follows a clear arithmetic progression. Each multiplier is $0.5$ greater than the previous one.

Calculating the Missing Term

Following the identified pattern, the next multiplier should be $2.0 + 0.5 = 2.5$.

To find the missing term (?), we multiply the last known term ($18$) by the next multiplier ($2.5$):

Calculation: $18 \times 2.5 = 18 \times \frac{5}{2}$

Alternatively, $18 \times 2.5 = 18 \times (2 + 0.5) = (18 \times 2) + (18 \times 0.5) = 36 + 9 = 45$.

So, the missing term in the series is $45$. The complete series is $12, 6, 6, 9, 18, 45$.