Finding the Missing Number in a Series

The question asks us to find the number that replaces the question mark in the given series:

6, 6, 8, 24, 28, 140, ?

To solve number series problems, we look for a pattern or a rule that connects consecutive numbers in the sequence. Let's examine the relationship between each pair of adjacent numbers.

Analyzing the Number Series Pattern

Let's look at the operations performed to get from one number to the next:

• From the 1st term (6) to the 2nd term (6): $6 \rightarrow 6$. This could be $6 + 0$ or $6 \times 1$.
• From the 2nd term (6) to the 3rd term (8): $6 \rightarrow 8$. This is $6 + 2$.
• From the 3rd term (8) to the 4th term (24): $8 \rightarrow 24$. This is $8 \times 3$.
• From the 4th term (24) to the 5th term (28): $24 \rightarrow 28$. This is $24 + 4$.
• From the 5th term (28) to the 6th term (140): $28 \rightarrow 140$. This is $28 \times 5$.

Let's summarize the operations found:

• Term 1 to Term 2: $\times 1$ ($6 \times 1 = 6$)
• Term 2 to Term 3: $+ 2$ ($6 + 2 = 8$)
• Term 3 to Term 4: $\times 3$ ($8 \times 3 = 24$)
• Term 4 to Term 5: $+ 4$ ($24 + 4 = 28$)
• Term 5 to Term 6: $\times 5$ ($28 \times 5 = 140$)

We can observe a clear pattern here:

• The operations are alternating between multiplication and addition.
• The number used in the operation is increasing by 1 each time (1, 2, 3, 4, 5).

The pattern is: $\times 1, + 2, \times 3, + 4, \times 5, \dots$

Applying the Pattern to Find the Next Number

Following this established pattern, the next operation after $\times 5$ should be $+ 6$. We need to apply this operation to the last number in the series, which is 140.

The next number will be: $140 + 6$

$140 + 6 = 146$

Therefore, the number that replaces the question mark is 146.

Conclusion

The series follows the pattern of alternating multiplication and addition with consecutive integers starting from 1. Applying the next step in the pattern ($\boldsymbol{+6}$) to the last number ($\boldsymbol{140}$) gives us the missing number, which is $\boldsymbol{146}$.

Revision Table: Number Series Patterns

Understanding different types of number series patterns is crucial for solving these questions. Here are a few common types:

Additional Information: Solving Number Series Questions

Solving number series problems often involves careful observation and trial and error. Here are some tips:

• Look for simple arithmetic operations: Check for constant addition, subtraction, multiplication, or division.
• Examine differences/ratios: If the simple operations don't work, find the differences or ratios between consecutive terms. See if these differences/ratios form a pattern.
• Check for alternating patterns: The pattern might switch between two different operations or values.
• Consider squares, cubes, and prime numbers: The series might involve squares or cubes of numbers, or a sequence of prime numbers.
• Combine patterns: Sometimes, the pattern is a combination of two or more simple patterns.
• Practice: Solving many different types of number series problems helps you recognize patterns more quickly.