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.
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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
