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What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295?
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What should be come in place of "?" in the given series? 10,19,?,199,7...
Understanding the Series
To identify the missing number in the series: 10, 19, ?, 199, 775, 3079, 12295, we need to analyze the relationship between the numbers.
Analyzing Differences
Let's calculate the differences between consecutive terms:
- From 10 to 19: 19 - 10 = 9
- From 19 to ?: Let’s denote the missing number as x.
- From x to 199: 199 - x
- From 199 to 775: 775 - 199 = 576
- From 775 to 3079: 3079 - 775 = 2304
- From 3079 to 12295: 12295 - 3079 = 9216
Now we have a new series of differences: 9, (199 - x), 576, 2304, 9216.
Identifying Patterns
The differences appear to follow a pattern:
- 9 = 3^2
- 576 = 24^2
- 2304 = 48^2
- 9216 = 96^2
It seems the differences are the squares of multiples of 3.
Finding the Missing Difference
To find the missing difference (199 - x), we notice the pattern of squares doubles:
- The next difference before 576 should be 36 (6^2).
Thus, we set up the equation:
199 - x = 36.
Solving for x gives:
x = 199 - 36 = 163.
Conclusion
The missing number in the series is 163. The complete series is 10, 19, 163, 199, 775, 3079, 12295.
To identify the missing number in the series: 10, 19, ?, 199, 775, 3079, 12295, we need to analyze the relationship between the numbers.
Analyzing Differences
Let's calculate the differences between consecutive terms:
- From 10 to 19: 19 - 10 = 9
- From 19 to ?: Let’s denote the missing number as x.
- From x to 199: 199 - x
- From 199 to 775: 775 - 199 = 576
- From 775 to 3079: 3079 - 775 = 2304
- From 3079 to 12295: 12295 - 3079 = 9216
Now we have a new series of differences: 9, (199 - x), 576, 2304, 9216.
Identifying Patterns
The differences appear to follow a pattern:
- 9 = 3^2
- 576 = 24^2
- 2304 = 48^2
- 9216 = 96^2
It seems the differences are the squares of multiples of 3.
Finding the Missing Difference
To find the missing difference (199 - x), we notice the pattern of squares doubles:
- The next difference before 576 should be 36 (6^2).
Thus, we set up the equation:
199 - x = 36.
Solving for x gives:
x = 199 - 36 = 163.
Conclusion
The missing number in the series is 163. The complete series is 10, 19, 163, 199, 775, 3079, 12295.
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What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295?
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What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295?.
What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What should be come in place of "?" in the given series? 10,19,?,199,775,3079,12295?.
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