Solving the Number Series: 45, 49, 58, 74, ...

The question asks us to find the missing number in the given series: 45, 49, 58, 74.

We need to identify the pattern by looking at the differences between consecutive terms:

• Difference between the 1st and 2nd term: $49 - 45 = 4$
• Difference between the 2nd and 3rd term: $58 - 49 = 9$
• Difference between the 3rd and 4th term: $74 - 58 = 16$

Identifying the Pattern

The differences found are 4, 9, and 16. Observe that these numbers are perfect squares:

• $4 = 2^2$
• $9 = 3^2$
• $16 = 4^2$

The pattern suggests that the differences are squares of consecutive integers starting from 2.

Calculating the Missing Term

Following this pattern, the next difference should be the square of the next integer, which is 5:

• Next difference = $5^2 = 25$

To find the missing term in the series, add this difference to the last known term (74):

• Missing term = $74 + 25$
• Missing term = $99$

Therefore, the correct option completing the series is 99.