Question

Find out the wrong term in the given series.
220, 108, 56, 24, 10, 3

• A. 108
• B. 56
• C. 24
• D. 3

Hint:

For finding the wrong term in a series: {Look for Consistent Patterns:} Identify arithmetic, geometric, or mixed operations between consecutive terms (addition, subtraction, multiplication, division, squares, cubes, etc.).

Answer 1

The Correct Option is B

Step 1: Analyze the given numerical series.
The series is: 220, 108, 56, 24, 10, 3.
The numbers are decreasing, suggesting operations like subtraction or division. Let's look for a pattern by examining the relationship between consecutive terms. It's often easier to find patterns by working from the smaller numbers (right to left) for decreasing series, or by trial and error with common arithmetic/geometric operations.
Step 2: Test for a consistent pattern by working backwards (from right to left).
Let's assume the pattern is of the form $x \times k + C$ or $x/k + C$.
Consider the transformation from 3 to 10:
$3 \times 2 = 6$, $6 + 4 = 10$
So, the operation could be ($\times 2 + 4$). Let's test this forward.
Step 3: Apply the identified pattern consistently from right to left.
Starting from the last term, 3:

• From 3 to 10: $3 \times 2 + 4 = 6 + 4 = 10$. (This matches the series)
• From 10 to 24: $10 \times 2 + 4 = 20 + 4 = 24$. (This matches the series)
• From 24 to the next expected term: $24 \times 2 + 4 = 48 + 4 = 52$.

According to this consistent pattern, the term after 24 should be 52. However, the given series has 56 at this position. This indicates that 56 might be the wrong term.
Step 4: Verify the rest of the series using the corrected term.
If 52 was the correct term instead of 56:

• From 52 to 108: $52 \times 2 + 4 = 104 + 4 = 108$. (This matches the series)
• From 108 to 220: $108 \times 2 + 4 = 216 + 4 = 220$. (This matches the series)

The pattern "$x \times 2 + 4$" holds true for all other terms if 56 is replaced by 52.
Step 5: Identify the wrong term.
The term that breaks the consistent pattern is 56, as it should be 52. The final answer is $\boxed{\text{(2)}}$.