A number series is given with one term missing. Using the observed pattern, choose the correct option to complete the series: 18, 25, 34, 45, ?

Introduction / Context:
This question is a classic example of a number series based on increasing differences. Instead of directly applying a formula to the terms, we look at how each term changes relative to the previous one. Many reasoning questions rely on such difference patterns, so it is important to become comfortable with spotting them quickly.

Given Data / Assumptions:
The series provided is:
18, 25, 34, 45, ?
We assume that there is a consistent pattern in the differences between consecutive terms, and we must extend this pattern to find the missing number.

Concept / Approach:
The main idea is to compute the difference between consecutive terms and see if these differences themselves form a recognizable pattern. Often these differences increase or decrease in a simple manner, such as adding a constant amount or following their own arithmetic progression.

Step-by-Step Solution:
Step 1: Compute the first differences between consecutive terms.25 - 18 = 734 - 25 = 945 - 34 = 11Step 2: Observe the pattern in the differences: 7, 9, 11. These are consecutive odd numbers.Step 3: The next difference should continue this pattern of odd numbers. After 7, 9, and 11, the next odd number is 13.Step 4: Add this next difference to the last known term.45 + 13 = 58.

Verification / Alternative check:
We can quickly verify by reconstructing the series from 18 using the observed pattern of odd differences: 18 + 7 = 25, 25 + 9 = 34, 34 + 11 = 45, and 45 + 13 = 58. Everything is consistent, confirming that the missing term must be 58 if the series is to preserve the pattern of increasing odd differences.

Why Other Options Are Wrong:
60, 59, 65, and 52 do not maintain the odd difference progression 7, 9, 11, 13. For example, if we chose 60, the final difference would be 15, which jumps ahead, and the sequence of differences becomes 7, 9, 11, 15, breaking the neat pattern. The other options distort the difference sequence even more noticeably.

Common Pitfalls:
Students sometimes search for multiplicative or more complex rules when a simple difference pattern is sufficient. Another mistake is miscalculating one of the differences, which then leads to an incorrect next term. Always compute the differences carefully and check whether they follow a simple and consistent pattern before deciding on the answer.

Final Answer:
The missing term that correctly completes the series is 58.