Solving the Number Series Pattern

The given series is 4, 11, 25, 46, 74, X. We need to find the value of X by identifying the underlying pattern in the sequence of numbers.

Finding the Pattern in the Series

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

• Difference between the 2nd and 1st term: ${11 - 4 = 7}$
• Difference between the 3rd and 2nd term: ${25 - 11 = 14}$
• Difference between the 4th and 3rd term: ${46 - 25 = 21}$
• Difference between the 5th and 4th term: ${74 - 46 = 28}$

The differences we found are 7, 14, 21, and 28. Let's look at these differences:

${7, 14, 21, 28, \dots}$

We can observe that this sequence of differences is itself an arithmetic progression. The common difference in this sequence is ${14 - 7 = 7}$, ${21 - 14 = 7}$, and ${28 - 21 = 7}$.

Determining the Next Term in the Number Series

Since the differences are increasing by 7 each time, the next difference in the sequence of differences should be ${28 + 7 = 35}$.

To find the next term (X) in the original series, we add this next difference (35) to the last term of the original series (74).

${X = 74 + 35}$

${X = 109}$

Therefore, the number that should come in place of X in the given series is 109.

Revision Table: Number Series Analysis

Additional Information on Number Series Patterns

Number series questions are common in aptitude tests and assess logical reasoning abilities. There are many different types of patterns that can appear in number series, including:

• Arithmetic Progression: Each term is obtained by adding a constant value to the previous term.
• Geometric Progression: Each term is obtained by multiplying the previous term by a constant value.
• Differences: The pattern is found by looking at the differences between consecutive terms (like in this problem). The differences themselves might form an arithmetic series, geometric series, squares, cubes, etc.
• Alternating Series: The series might follow two different patterns alternately.
• Fibonacci Series or similar: Each term is the sum of the previous two terms (or a variation of this rule).
• Squares or Cubes: The terms might be squares or cubes of numbers, possibly with some addition or subtraction.

Solving number series requires careful observation, calculating differences, ratios, or other relationships between terms to identify the rule governing the sequence.