Number Series Analysis: Finding the Missing Term

This problem requires us to identify the pattern in the given number series and use it to find the missing number represented by the question mark (?). The series provided is: 24.9, 23.6, 21, 17.1, ?, 5.4.

Identifying the Pattern in the Series

To find the missing number, let's examine the differences between consecutive terms in the series:

• Difference between the 1st and 2nd term: $24.9 - 23.6 = 1.3$
• Difference between the 2nd and 3rd term: $23.6 - 21 = 2.6$
• Difference between the 3rd and 4th term: $21 - 17.1 = 3.9$

Now, let's look at these differences: 1.3, 2.6, 3.9.

We can observe a pattern in these differences themselves. Each difference is 1.3 more than the previous one:

• $1.3$
• $1.3 + 1.3 = 2.6$
• $2.6 + 1.3 = 3.9$

This indicates that the amount being subtracted from the series terms is increasing by 1.3 each time. These amounts can be represented as $1.3 \times 1$, $1.3 \times 2$, $1.3 \times 3$, and so on.

Calculating the Missing Term

Following the identified pattern, the next difference to subtract should be $3.9 + 1.3 = 5.2$.

So, the missing term (?) is calculated by subtracting 5.2 from the previous term (17.1):

Missing Term $= 17.1 - 5.2 = 11.9$

Verifying the Next Term

To ensure our pattern is correct, let's calculate the difference after 5.2. It should be $5.2 + 1.3 = 6.5$.

Now, let's subtract this difference (6.5) from our calculated missing term (11.9):

Next Term $= 11.9 - 6.5 = 5.4$

This matches the last number given in the series, confirming our pattern and calculation.

Summary Table

Therefore, the number that replaces the question mark (?) in the series is 11.9.