Solving the Number Series Problem

The given number series is 5475, 1100, 225, 50, ?, 8, 6.6. We need to find the number that replaces the question mark.

Let's analyze the pattern in the given number series. We observe that the numbers are decreasing. Let's look for a relationship between consecutive terms.

Identifying the Number Series Pattern

Let's examine the transition from one number to the next:

• From 5475 to 1100
• From 1100 to 225
• From 225 to 50
• From 50 to ?
• From ? to 8
• From 8 to 6.6

The decrease is quite significant at the beginning, suggesting division. Let's try dividing a term by the next one, or dividing by a fixed number and adding/subtracting something.

Let's try dividing the previous term by 5 and see the result:

• $ \frac{5475}{5} = 1095 $. The next term is 1100. The difference is $1100 - 1095 = 5$.
• $ \frac{1100}{5} = 220 $. The next term is 225. The difference is $225 - 220 = 5$.
• $ \frac{225}{5} = 45 $. The next term is 50. The difference is $50 - 45 = 5$.

It appears the pattern is to divide the previous term by 5 and then add 5 to get the next term. Let's verify this pattern with a formula:

If $T_n$ is the n-th term, then $T_{n+1} = \frac{T_n}{5} + 5$.

Applying the Pattern to Find the Missing Number

Let's apply this pattern to find the missing term after 50.

The term before the question mark is 50 (which is $T_4$). The missing term is $T_5$.

Using the formula:

$T_5 = \frac{T_4}{5} + 5$

$T_5 = \frac{50}{5} + 5$

$T_5 = 10 + 5$

$T_5 = 15$

So, the missing number is 15.

Verifying the Pattern with Subsequent Terms

Let's check if the pattern holds for the terms after 15 (which is $T_5$). The next term is 8 ($T_6$).

$T_6 = \frac{T_5}{5} + 5$

$T_6 = \frac{15}{5} + 5$

$T_6 = 3 + 5$

$T_6 = 8$ (This matches the given term 8).

The next term is 6.6 ($T_7$).

$T_7 = \frac{T_6}{5} + 5$

$T_7 = \frac{8}{5} + 5$

$T_7 = 1.6 + 5$

$T_7 = 6.6$ (This matches the given term 6.6).

The pattern $T_{n+1} = \frac{T_n}{5} + 5$ is consistent throughout the series.

Conclusion

The number that replaces the question mark in the series 5475, 1100, 225, 50, ?, 8, 6.6 is 15.

Number Series Pattern Analysis Revision

Additional Information on Number Series Questions

Number series questions are common in aptitude tests and competitive exams. They test your ability to identify patterns in a sequence of numbers.

Common types of patterns include:

• Arithmetic series (constant difference between terms)
• Geometric series (constant ratio between terms)
• Mixed series (combination of arithmetic and geometric operations)
• Difference series (pattern in the differences between terms)
• Double difference series (pattern in the differences of the differences)
• Square or Cube series (terms are squares or cubes or related to them)
• Fibonacci or similar series (each term is the sum of the previous two or more terms)
• Alternating patterns (different patterns applied to alternate terms)

To solve number series problems, it is helpful to:

• Look for simple arithmetic operations (addition, subtraction, multiplication, division).
• Look for a constant difference or ratio.
• Examine the differences between consecutive terms.
• Consider squares, cubes, or other powers.
• Check for alternating patterns.
• If numbers are decreasing rapidly, think about division or subtraction of a growing number.
• If numbers are decreasing slowly, think about subtraction or division by a larger number.

Practice is key to improving your ability to quickly spot the pattern in a number series.