Final answer:
The missing number in the series is 64, which follows the pattern observed in the changes between the numbers of halving and then multiplying by 1.5, offset by adding or subtracting 8.
Step-by-step explanation:
To find the missing number in the series 48, 24, 32, 40, 32, 56, we need to observe the pattern between the numbers. Let's look at the changes between successive numbers:
- 48 to 24 is a decrease by 24.
- 24 to 32 is an increase by 8.
- 32 to 40 is an increase by 8 as well.
- Now observe that 40 decreasing to 32 is a decrease by 8.
Since we see the alternating pattern of doubling and then adding/subtracting 8, applying this logic, the pattern should continue with another doubling:
- 32 (previous number) × 2 = 64
So the missing number in the sequence is 64, and we can now see the series forms a pattern of halving and then multiplying by 1.5 (48, 24, 36, 40) offset by adding or subtracting 8.