Number Series Pattern Analysis

The goal is to find the missing number in the sequence: 65, 40, 24, 15, 11, ?.

Step 1: Calculate Differences Between Terms

Calculate the difference between consecutive numbers:

• $65 - 40 = 25$
• $40 - 24 = 16$
• $24 - 15 = 9$
• $15 - 11 = 4$

The resulting sequence of differences is: 25, 16, 9, 4.

Step 2: Identify the Pattern in Differences

Recognize the pattern within the differences:

• $25 = 5^2$
• $16 = 4^2$
• $9 = 3^2$
• $4 = 2^2$

The differences are consecutive perfect squares, decreasing from $5^2$.

Step 3: Determine the Next Difference

Following the pattern, the next square should be $1^2$.

• $1^2 = 1$

This means the next difference in the original series is 1.

Step 4: Calculate the Missing Number

Subtract this next difference (1) from the last term of the series (11):

• $11 - 1 = 10$

Therefore, the number that should replace the question mark is 10.