What number would replace question mark (?) in the series below?

1.5, 4, 7.5, 12, 17.5, 24, 31.5, ?

The correct answer is 40.

To find the missing number, let's carefully examine the pattern hidden within the series:

Given Series: 1.5, 4, 7.5, 12, 17.5, 24, 31.5, ?

Step 1: Find the differences between consecutive terms.

4 - 1.5 = 2.5
7.5 - 4 = 3.5
12 - 7.5 = 4.5
17.5 - 12 = 5.5
24 - 17.5 = 6.5
31.5 - 24 = 7.5

Step 2: Identify the pattern in the differences.

The differences are: 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, ...

This is itself an arithmetic sequence where each difference increases by 1 each time. So the next difference in the sequence must be:

$7.5+1=8.5$

Step 3: Apply the next difference to find the missing term.

$31.5+8.5=40$

Step 4: Verify the full pattern.

Term 1: 1.5
Term 2: 1.5 + 2.5 = 4 ✓
Term 3: 4 + 3.5 = 7.5 ✓
Term 4: 7.5 + 4.5 = 12 ✓
Term 5: 12 + 5.5 = 17.5 ✓
Term 6: 17.5 + 6.5 = 24 ✓
Term 7: 24 + 7.5 = 31.5 ✓
Term 8: 31.5 + 8.5 = 40 ✓

The rule is clear: each consecutive difference increases by 1, starting from 2.5. This gives us the 8th term as 40.