A number series is given with one term missing. Using the observed rule, select the correct number to complete the series: 10, 22, 46, ?

Introduction / Context:
This question involves a number series that follows a simple multiplicative and additive rule. Many exam series questions use a combination of doubling, halving, or adding a constant to generate each next term. Quickly detecting such a pattern helps in solving these questions efficiently.

Given Data / Assumptions:
The series provided is:
10, 22, 46, ?
We assume that each consecutive term is generated from the previous one by applying a consistent operation, most likely involving multiplication by a fixed factor and then addition or subtraction of a small constant.

Concept / Approach:
The natural first check is whether each term is approximately double the previous term. If so, we then examine whether a small correction, such as adding or subtracting a fixed number, is applied. This approach is common in reasoning questions where numbers grow relatively fast but not purely exponentially.

Step-by-Step Solution:
Step 1: Compare 10 and 22.10 multiplied by 2 gives 20, and then adding 2 gives 22. So, 10 * 2 + 2 = 22.Step 2: Compare 22 and 46.22 multiplied by 2 gives 44, and adding 2 gives 46. So, 22 * 2 + 2 = 46.Step 3: The pattern seems to be: new term = previous term * 2 + 2.Step 4: Apply the same rule to find the missing term.46 * 2 + 2 = 92 + 2 = 94.

Verification / Alternative check:
We can confirm by working backwards as well. If we take 94 and attempt the inverse operation, we subtract 2 and then divide by 2: (94 - 2) / 2 = 92 / 2 = 46, which matches the previous term. Applying this inverse logic again to 46 gives (46 - 2) / 2 = 22. This backward consistency supports our conclusion that the rule is correct.

Why Other Options Are Wrong:
Values like 90, 91, 95, and 88 do not satisfy the relation new term = previous term * 2 + 2. For example, 46 * 2 + 2 is not 90, 91, 95, or 88. Using any of them would break the precise pattern observed between earlier terms, which is not acceptable in a well formed series question.

Common Pitfalls:
One common error is to assume a constant difference between terms, which clearly does not hold here. Another is to approximate and think that because 22 is a little more than double 10 and 46 is a little more than double 22, any value around twice 46 is acceptable. However, the series relies on an exact recurrence, so minor deviations are not allowed.

Final Answer:
The missing number that correctly completes the series is 94.