320, 225, 178, 155, 144, ?
Number Series Pattern Analysis: 320, 225, 178, 155, 144, ?
This problem requires us to identify the missing number in a given sequence. We need to find the pattern within the series 320, 225, 178, 155, 144, ?. Let's carefully examine the steps involved.
Series Differences Analysis
The first step is to calculate the difference between each consecutive pair of numbers:
| Term Pair | Calculation | Difference |
|---|---|---|
| 320 and 225 | $320 - 225$ | 95 |
| 225 and 178 | $225 - 178$ | 47 |
| 178 and 155 | $178 - 155$ | 23 |
| 155 and 144 | $155 - 144$ | 11 |
The sequence of differences we found is: 95, 47, 23, 11.
Difference Pattern Identification
Next, we analyze the pattern within this sequence of differences (95, 47, 23, 11). We look at the differences between these consecutive differences, often called the second differences:
- First second difference: $47 - 95 = -48$
- Second second difference: $23 - 47 = -24$
- Third second difference: $11 - 23 = -12$
Observing the second differences ( -48, -24, -12 ), we notice a consistent pattern: each subsequent difference is half of the previous one.
- $-48 \div 2 = -24$
- $-24 \div 2 = -12$
Series Number Calculation
To determine the next number in the original series, we first need to predict the next second difference. Based on the pattern, we divide the last second difference by 2:
Next second difference = $-12 \div 2 = -6$
Now, we use this value to find the next difference in the main series. The last difference calculated was 11. The next difference (the fifth difference in the sequence) is found by adding the last difference and the next second difference:
Next difference = $11 + (-6) = 5$
Finally, to find the missing number in the original series, we subtract this calculated difference (5) from the last known term (144):
Missing Number = $144 - 5 = 139$
Missing Number Conclusion
Therefore, the number that correctly replaces the question mark (?) in the series is 139.
Similar Questions
Which of the following numbers will replace the question mark (?) in the given series?
6, 8, 11, 16, ?, 34, 47, 64
Which number will replace the question mark (?) in the following series?
36, 512, 100, 1728, ?, 4096
Which number will replace the question mark (?) in the following series?
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Select the option that represents the letters which when sequentially placed from left to right in the blanks below will complete the letter series.
P _ I _ Y _ O _ U Y P _ K U _ P O _ _ Y
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Which number will replace the question mark (?) in the following series?
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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
