Understanding the Number Series

The question asks us to find the missing number in the given sequence: 23, 24, 32, 59, ?, 248. We need to identify the pattern governing this series to determine the correct number.

Identifying the Pattern

Let's examine the difference between consecutive terms in the series:

• Term 2 - Term 1: $24 - 23 = 1$
• Term 3 - Term 2: $32 - 24 = 8$
• Term 4 - Term 3: $59 - 32 = 27$

Now, let's look at these differences: 1, 8, 27. We can observe that these numbers are perfect cubes:

• $1 = 1^3$
• $8 = 2^3$
• $27 = 3^3$

The pattern suggests that the difference between consecutive terms is increasing based on the cube of consecutive integers starting from 1.

Calculating the Missing Term

Following the identified pattern, the difference between the fifth term (the missing number) and the fourth term (59) should be the next cube in the sequence, which is $4^3$.

• Calculate $4^3$: $4 \times 4 \times 4 = 64$.
• Add this difference to the fourth term: $59 + 64 = 123$.

So, the missing number is likely 123.

Verifying the Pattern

Let's verify if this fits the rest of the series. The next difference should be $5^3$.

• Calculate $5^3$: $5 \times 5 \times 5 = 125$.
• Add this difference to our calculated missing term (123): $123 + 125 = 248$.

This result, 248, matches the last term in the given series. Therefore, the pattern is confirmed, and the missing number is 123.

Series Conclusion

The complete series is: 23, 24, 32, 59, 123, 248.