Finding the Missing Number in the Series

The question asks us to identify the pattern in the given number series and find the next number.

The series is: 18, 54, 29, 87, 62, 186, ?

Let's look at the relationship between the numbers in the series:

• Starting with the first number, 18.
• The second number is 54. We can see that \(18 \times 3 = 54\).
• The third number is 29. We can see that \(54 - 25 = 29\).
• The fourth number is 87. We can see that \(29 \times 3 = 87\).
• The fifth number is 62. We can see that \(87 - 25 = 62\).
• The sixth number is 186. We can see that \(62 \times 3 = 186\).

It appears there is a repeating pattern of two operations:

1. Multiply the current number by 3.
2. Subtract 25 from the result of the previous step.

Let's verify the pattern with the given series:

• Step 1: \(18 \times 3 = 54\) (Correct)
• Step 2: \(54 - 25 = 29\) (Correct)
• Step 3: \(29 \times 3 = 87\) (Correct)
• Step 4: \(87 - 25 = 62\) (Correct)
• Step 5: \(62 \times 3 = 186\) (Correct)

The pattern is consistent. The last number given is 186. Following the pattern, the next operation should be to subtract 25.

To find the number that replaces the question mark (?), we apply the next step in the pattern:

Missing number = Last number \( - 25\)

Missing number = \(186 - 25\)

Missing number = \(161\)

Thus, the number that replaces the question mark is 161.

Revision Table: Number Series Pattern

Here's a breakdown of the steps and the pattern observed in the series:

• 1st number: 18
• 2nd number: \(18 \times 3 = 54\)
• 3rd number: \(54 - 25 = 29\)
• 4th number: \(29 \times 3 = 87\)
• 5th number: \(87 - 25 = 62\)
• 6th number: \(62 \times 3 = 186\)
• 7th number (missing): \(186 - 25 = 161\)

Additional Information: Solving Number Series Questions

Solving number series problems requires finding the rule or pattern that connects the numbers. Common patterns include:

• Arithmetic Progression (addition or subtraction of a constant value).
• Geometric Progression (multiplication or division by a constant value).
• Differences between consecutive numbers (first differences, second differences, etc.).
• Alternating patterns (different rules applied to alternate terms).
• Combination of operations (like in this problem: multiplication and subtraction).
• Patterns involving squares, cubes, prime numbers, or Fibonacci sequences.

To solve number series questions effectively:

• Look for differences or ratios between consecutive numbers.
• Check for patterns in alternate numbers.
• Try combining simple arithmetic operations.
• If the numbers grow or shrink rapidly, consider multiplication, division, squares, or cubes.
• Practice recognizing common sequences.