Which number will complete the following increasing number series by continuing the same arithmetic pattern: 63, 72, 81, 90, ____, 108?

Introduction / Context:
This is a straightforward arithmetic series question. The numbers 63, 72, 81, 90, ____, 108 increase in a very regular manner, suggesting a constant difference between consecutive terms. Such questions are common warm up problems in number series sections and help build speed and confidence.

Given Data / Assumptions:

• Series: 63, 72, 81, 90, ?, 108.
• Options: 80, 99, 100, 117.
• We assume a simple and consistent pattern such as equal differences.

Concept / Approach:
For regularly spaced numbers like these, the best first step is to calculate the difference between consecutive terms. If the difference is constant, the series is arithmetic. If the difference itself changes in a simple pattern, we examine that instead. Here, we will see that the difference is the same at every step, which makes the missing term easy to identify.

Step-by-Step Solution:
Step 1: Compute consecutive differences.72 - 63 = 9.81 - 72 = 9.90 - 81 = 9.Step 2: Identify the pattern.Each term increases by 9, so this is an arithmetic progression with common difference 9.Step 3: Continue the pattern.Missing term after 90 = 90 + 9 = 99.Step 4: Check final term.Next term after 99 = 99 + 9 = 108, which matches the given last term and confirms the pattern.

Verification / Alternative check:
Write the complete series using the found term: 63, 72, 81, 90, 99, 108. Now check every step: 72, 81, 90, 99, 108 are all exactly 9 more than the preceding term. There are no exceptions, so the rule holds throughout and the answer is fully consistent.

Why Other Options Are Wrong:
80: Would give a difference of -10 from 90 to 80 and then +28 to 108, which clearly breaks the pattern.100: Would produce a difference of 10 from 90 and only 8 from 100 to 108, so differences would not be equal.117: Would be 27 more than 90 and 9 more than 108, which does not fit any simple, consistent rule.

Common Pitfalls:
Because the numbers are multiples of 9, some students overcomplicate the question by bringing in divisibility or factor properties. In reality, just checking the simple difference between consecutive terms is enough. Always try the most basic pattern first before looking for more complex ones.

Final Answer:
The missing number that keeps a constant difference of 9 is 99.