Question

Find the missing number: 5, 7, 13, 25, 45, ________

Hint:

When number differences increase regularly, always check the second-level pattern.

Answer 1

Step 1: Find the differences between consecutive terms.
\[ 7 - 5 = 2,\quad 13 - 7 = 6,\quad 25 - 13 = 12,\quad 45 - 25 = 20 \]
Step 2: Analyze the pattern of differences.
The differences are:
\[ 2,\; 6,\; 12,\; 20 \]
These increase by:
\[ +4,\; +6,\; +8 \]
Step 3: Find the next difference.
Following the pattern, the next increase will be \( +10 \), so:
\[ 20 + 10 = 30 \]
Step 4: Find the missing number.
\[ 45 + 30 = 75 \]
Step 5: Conclusion.
The missing number in the series is 75.