The next term in the series 0, 1, 9, 36, 100, ______ is:
225
To identify the next term in the given series: 0, 1, 9, 36, 100, ______, we need to determine the pattern or rule governing the series.
Let's analyze the given terms:
- 0: This is the square of 0. \(0^2 = 0\)
- 1: This is the square of 1. \(1^2 = 1\)
- 9: This is the square of 3. \(3^2 = 9\)
- 36: This is the square of 6. \(6^2 = 36\)
- 100: This is the square of 10. \(10^2 = 100\)
The series appears to be the square of consecutive triangular numbers. Triangular numbers are those which can form an equilateral triangle. The sequence of triangular numbers is: 0, 1, 3, 6, 10, 15, ...
Let's calculate the next triangular number after 10:
- The triangular number after \(10\) is \(15\).
Therefore, the next term in the series, which is the square of this triangular number, is:
- \(15^2 = 225\)
Thus, the next term in the series is 225. Hence, the correct answer is 225.
Similar Questions
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If the series 4, 5, 8, 13, 14, 17, 22, .... is continued in the same pattern, which one of the following is not a term of this series?
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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, ?
