Finding the Wrong Number in a Series

The question asks us to identify the number that does not fit the pattern in the given series:

6, 12, 20, 32, 42, 56, 72

Analyzing the Number Series Pattern

To find the wrong number, let's look at the difference between consecutive terms in the series. This often reveals the underlying pattern.

• Difference between 12 and 6: $12 - 6 = 6$
• Difference between 20 and 12: $20 - 12 = 8$
• Difference between 32 and 20: $32 - 20 = 12$
• Difference between 42 and 32: $42 - 32 = 10$
• Difference between 56 and 42: $56 - 42 = 14$
• Difference between 72 and 56: $72 - 56 = 16$

The differences are 6, 8, 12, 10, 14, 16.

Let's examine this sequence of differences: 6, 8, 12, 10, 14, 16. If we look closely, there seems to be a pattern where the differences increase by 2: 6, 8, 10, 12, 14, 16.

Let's assume the pattern is adding consecutive even numbers starting from 6.

Identifying the Deviation from the Pattern

Let's construct the series based on the identified pattern (adding 6, 8, 10, 12, 14, 16...):

• Starting term: 6
• Next term: $6 + 6 = 12$ (Matches the given series)
• Next term: $12 + 8 = 20$ (Matches the given series)
• Next term: $20 + 10 = 30$ (Expected number based on pattern)
• Next term: $30 + 12 = 42$ (Matches the given series)
• Next term: $42 + 14 = 56$ (Matches the given series)
• Next term: $56 + 16 = 72$ (Matches the given series)

Comparing the expected series (6, 12, 20, 30, 42, 56, 72) with the given series (6, 12, 20, 32, 42, 56, 72), we can see that the number 32 in the given series deviates from the expected number 30.

Therefore, the wrong number in the given series is 32.

The number 32 does not follow the pattern of adding consecutive even numbers to the previous term. It should be 30.

Revision Table: Wrong Number Series

Understanding different types of series patterns is crucial for solving such problems. Revisiting common patterns helps reinforce the concepts.

• Arithmetic Series (constant difference)
• Geometric Series (constant ratio)
• Difference Series (pattern in the differences between terms, as seen here)
• Combination Series (mix of operations)
• Square/Cube Series (involving squares or cubes of numbers)

Additional Information: Number Series Analysis

When tackling number series questions, try these steps:

• Look at the difference between adjacent numbers. Is it constant? Is there a pattern in the differences?
• Look at the ratio between adjacent numbers. Is it constant?
• Consider squares or cubes of numbers ($1^2, 2^2, 3^2,...$ or $1^3, 2^3, 3^3,...$) or numbers near squares/cubes ($n^2 \pm k$ or $n^3 \pm k$).
• Check for alternating patterns or multiple interleaved series.
• Sometimes the pattern involves prime numbers, composite numbers, or specific sequences like Fibonacci.
• Practice with various types of number series problems to build familiarity with common patterns.