Which of the following options should come in place of the question mark (?) in the given series?
75 15 24 34 45?
57
Finding the Missing Number in the Series
The question asks us to identify the next term in the numerical sequence: 75, 15, 24, 34, 45, ?
Analyzing the Series Pattern
To find the missing number, let's examine the relationship between consecutive terms in the series. We can calculate the difference between each term and the one that follows it:
- Difference between the second and first term: \(15 - 75 = -60\)
- Difference between the third and second term: \(24 - 15 = 9\)
- Difference between the fourth and third term: \(34 - 24 = 10\)
- Difference between the fifth and fourth term: \(45 - 34 = 11\)
Identifying the Pattern Logic
Let's look at the sequence of differences we found: -60, 9, 10, 11.
Notice that starting from the second difference (9), the differences form a simple arithmetic progression, increasing by 1 each time:
- The first difference is -60.
- The second difference is 9.
- The third difference is 10 (which is 9 + 1).
- The fourth difference is 11 (which is 10 + 1).
Following this established pattern, the next difference in the sequence should be 1 greater than the previous difference (11).
Calculating the Missing Term
The next difference should therefore be:
\(11 + 1 = 12\)To find the missing term (?), we add this next difference (12) to the last known term in the series (45):
\(45 + 12 = 57\)Conclusion
Thus, the number that should come in place of the question mark (?) in the given series is 57.
The complete series is 75, 15, 24, 34, 45, 57.
Similar Questions
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175 221 267 313 359 ?
Which of the following options should come in place of the question mark (?) in the given series?
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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 ::?
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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 ::?
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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
