What will come in place of the question mark (?) in the given series?
614, ?, 349, 249, 168, 104
This question tests your ability to identify number patterns and sequences. Let's analyze the given series: 614, ?, 349, 249, 168, 104.
Observe the differences between consecutive numbers:
- Between 614 and 349: 614 - 349 = 265
- Between 349 and 249: 349 - 249 = 100
- Between 249 and 168: 249 - 168 = 81
- Between 168 and 104: 168 - 104 = 64
Notice that the differences themselves form a sequence: 265, 100, 81, 64. Let's analyze the differences between these differences:
- 265 - 100 = 165
- 100 - 81 = 19
- 81 - 64 = 17
While the pattern isn't immediately obvious in terms of simple arithmetic progressions, let's try another approach. Let's look at the differences between consecutive terms. The differences are decreasing. To solve the problem, we can try to establish a logical relationship between consecutive numbers in the given sequence. It appears there isn't a readily apparent arithmetic or geometric progression. Let’s analyze options:
Let's assume the missing number is 470. Then the differences would be: 614 - 470 = 144; 470 - 349 = 121; 349 - 249 = 100; 249 - 168 = 81; 168 - 104 = 64. Notice that 144 = 122, 121 = 112, 100 = 102, 81 = 92, 64 = 82. This reveals a clear pattern: the differences are perfect squares of consecutive decreasing integers (12, 11, 10, 9, 8). Therefore, 470 fits the pattern perfectly.
Therefore, the number that comes in place of the question mark is 470.
Similar Questions
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Select the correct option that will fill in the blank and complete the 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
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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
