Select the number from among the given options that can replace the question mark(?) in the following series. 48, 52, 60, 72, 88, ?
108
Understanding the Number Series Pattern
The question asks us to find the next number in the given series: 48, 52, 60, 72, 88, ?. To solve this number series problem, we need to identify the underlying pattern or rule that governs the progression of the numbers.
Analyzing the Differences Between Consecutive Terms
Let's calculate the difference between each consecutive pair of numbers in the series:
- Difference between the 2nd and 1st term: $52 - 48 = 4$
- Difference between the 3rd and 2nd term: $60 - 52 = 8$
- Difference between the 4th and 3rd term: $72 - 60 = 12$
- Difference between the 5th and 4th term: $88 - 72 = 16$
We can see the sequence of differences is: 4, 8, 12, 16. Let's look at this new sequence of differences.
Identifying the Pattern in the Differences
Let's find the difference between consecutive terms in the sequence of differences (4, 8, 12, 16):
- Difference between 8 and 4: $8 - 4 = 4$
- Difference between 12 and 8: $12 - 8 = 4$
- Difference between 16 and 12: $16 - 12 = 4$
The difference between consecutive terms in the sequence of differences is constant and equal to 4. This indicates that the differences between the original series terms form an arithmetic progression with a common difference of 4.
Predicting the Next Term in the Number Series
Following the pattern of differences (4, 8, 12, 16), the next difference should be $16 + 4 = 20$.
To find the next term in the original series, we add this next difference (20) to the last term of the series (88).
Next term = Last term + Next difference
Next term = $88 + 20$
Next term = $108$
So, the number that replaces the question mark (?) is 108.
Let's summarize the pattern:
| Term | Value | Difference from previous term |
|---|---|---|
| 1st | 48 | - |
| 2nd | 52 | $52 - 48 = 4$ |
| 3rd | 60 | $60 - 52 = 8$ |
| 4th | 72 | $72 - 60 = 12$ |
| 5th | 88 | $88 - 72 = 16$ |
| 6th | ? | $88 + 20 = 108$ |
Conclusion for the Number Series
Based on the pattern identified, the next number in the series 48, 52, 60, 72, 88, ? is 108.
Revision Table: Understanding Series Patterns
| Series Type | Pattern Example | Description |
|---|---|---|
| Arithmetic Series | 2, 5, 8, 11, ... | Constant difference between consecutive terms. |
| Geometric Series | 3, 6, 12, 24, ... | Constant ratio between consecutive terms. |
| Difference Series (as seen here) | Differences form a pattern (e.g., arithmetic, geometric). | Analyzing the differences helps reveal the underlying rule. |
| Mixed Series | Combination of patterns. | May involve arithmetic, geometric, squares, cubes, etc. |
Additional Information on Number Series Problems
Solving number series problems often involves:
- Calculating differences between consecutive terms (first-level differences).
- If the first-level differences don't show a pattern, calculate differences of the differences (second-level differences). This series had a constant second-level difference.
- Checking for patterns involving squares, cubes, prime numbers, or Fibonacci sequence.
- Looking for alternating patterns or multiple independent series intertwined.
- Sometimes the pattern involves multiplication or division rather than addition or subtraction.
Practice with various types of number series is key to quickly identifying the pattern during exams.
Important Questions from Number Series
- In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Which numbers should replace X and Y so that the pattern followed by the two numbers on the left side of :: is the same as that on the right side of :: ?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding /subtracting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
X : 676 :: 17 : Y - Which of the following options should come in place of the question mark (?) in the given series to make it logically complete?
125, 128, 133, 140, 149,? - What should come in place of the question mark (?) in the given series?
801 800 792 765 701 ? - What should come in place of the question mark (?) in the given series?
101 110 121 134 149 ? - What should come in place of the question mark (?) in the given series?
40, 48, 58, 66, 76, ?
