Select the number from among the given options that can replace the question mark (?) in the following series. 4, 8, 11, 22, 25, 50, ?
53
Finding the Pattern in a Number Series
The question asks us to find the missing number in the series: 4, 8, 11, 22, 25, 50, ?
To solve this, we need to identify the pattern governing the sequence of numbers.
Analyzing the Number Series Pattern
Let's look at the relationship between consecutive terms in the given series:
- From 4 to 8: The number is multiplied by 2 ($4 \times 2 = 8$).
- From 8 to 11: The number is increased by 3 ($8 + 3 = 11$).
- From 11 to 22: The number is multiplied by 2 ($11 \times 2 = 22$).
- From 22 to 25: The number is increased by 3 ($22 + 3 = 25$).
- From 25 to 50: The number is multiplied by 2 ($25 \times 2 = 50$).
The pattern observed is an alternating sequence of operations: first, multiply the number by 2, and then add 3 to the result to get the next number. This sequence of operations ($\times 2$, $+ 3$) repeats throughout the series.
Applying the Pattern to Find the Missing Number
The last operation performed was multiplication by 2 (from 25 to 50). Following the alternating pattern, the next operation must be adding 3.
So, to find the number that replaces the question mark (?), we need to add 3 to the last known term in the series, which is 50.
Calculation:
$50 + 3 = 53$
Therefore, the next number in the series is 53.
Step-by-Step Solution for the Number Series
Let $T_n$ represent the n-th term in the series.
- Identify the first two steps: $T_1 = 4$, $T_2 = 8$. $8 = 4 \times 2$. Operation: $\times 2$.
- Identify the next step: $T_2 = 8$, $T_3 = 11$. $11 = 8 + 3$. Operation: $+ 3$.
- Identify the next step: $T_3 = 11$, $T_4 = 22$. $22 = 11 \times 2$. Operation: $\times 2$.
- Identify the next step: $T_4 = 22$, $T_5 = 25$. $25 = 22 + 3$. Operation: $+ 3$.
- Identify the next step: $T_5 = 25$, $T_6 = 50$. $50 = 25 \times 2$. Operation: $\times 2$.
- Determine the next operation in the repeating sequence ($\times 2$, $+ 3$). Since the last operation was $\times 2$, the next must be $+ 3$.
- Apply the next operation to the last term ($T_6 = 50$): $T_7 = 50 + 3$.
- Calculate the result: $T_7 = 53$.
The missing number is 53.
| Step | Terms | Operation | Result |
|---|---|---|---|
| 1 | 4, 8 | $4 \times 2$ | 8 |
| 2 | 8, 11 | $8 + 3$ | 11 |
| 3 | 11, 22 | $11 \times 2$ | 22 |
| 4 | 22, 25 | $22 + 3$ | 25 |
| 5 | 25, 50 | $25 \times 2$ | 50 |
| 6 | 50, ? | $50 + 3$ | 53 |
Revision Table: Number Series Concepts
| Concept | Description | Example Pattern |
|---|---|---|
| Arithmetic Series | Adding or subtracting a constant difference. | 2, 5, 8, 11 (+3) |
| Geometric Series | Multiplying or dividing by a constant ratio. | 3, 6, 12, 24 ($\times 2$) |
| Mixed Operations Series | Combining arithmetic and geometric operations or other rules in a pattern. | 4, 8, 11, 22, 25, 50 ($\times 2, + 3$) |
| Difference Series | Looking at the differences between consecutive terms to find a pattern. | 1, 4, 9, 16 (Differences: 3, 5, 7 - pattern is +2) |
Additional Information on Number Series Problems
Number series questions are common in reasoning and aptitude tests. They assess your ability to identify logical patterns in sequences of numbers.
Solving these problems often involves:
- Looking at the difference between consecutive terms.
- Looking at the ratio between consecutive terms.
- Checking for alternating patterns of operations (like in this question).
- Checking for patterns involving squares, cubes, prime numbers, or Fibonacci sequence.
- Looking at patterns involving the position of the term (n-th term).
Practicing different types of number series helps in quickly recognizing the underlying logic.
Similar Questions
Select the number that will replace the question mark (?) in the following series.
12, 2, 24, 3, 72, 4, ?
Study the number that will replace the question mark (?) in the following series.
44, 22, 22, 33, 66, ?
Select the number that will replace the question mark (?) in the following series.
58, 60, 63, 68, 75, 86, ?
Select the number that will replace the question mark (?) in the following series.
8, 17, 36, 75, 154, ?
- Select the number that will replace the question mark (?) in the following figure series. 7, 7, 14, 42, ?, 840
Which number will replace the question mark (?) in the following series?
2, 12, 30, ?, 90, 132
Which of the following numbers will replace the question mark (?) in the given series?
98, 118, 140, ?, 190, 218
Which of the following numbers will replace the question mark (?) in the given series?
3, 7, 5, 61, 363 ?
Which of the following numbers will replace the question mark (?) in the given series?
7, 15, 30, 62, 125, 253, ?
Select the number from among the given options that can replace the question mark(?) in the following series.
2, 4, 7, 11, 16, 22, ?
Important Questions from Number Series
What will come in place of question mark (?) in the following number series?
2, 5, 11, 23, 44, 77, ?
What will come in place of question mark (?) in the following number series?
31, 32, 36, ?, 61, 86
What will come in the place of question mark (?) in the following number series?
3, 6, 18, ?, 630, 6930
What should come in place of the question mark ‘?’ in the following number series?
60, 40, 50, ?, 180, 460
A series is given with one term wrong. Select that wrong term from the given alternatives.
J12, M24, P48, S96, U192
