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Look at this series: 12, 80, 252, 576....... What number should come next?1100100820701180

Question

Look at this series: 12, 80, 252, 576....... What number should come next?1100100820701180

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Solution

This series seems to be increasing exponentially. To find the pattern, let's look at the differences between each pair of numbers:

80 - 12 = 68 252 - 80 = 172 576 - 252 = 324

These differences don't form a consistent pattern, so let's try looking at the ratios between each pair of numbers:

80 / 12 = 6.67 (approximately) 252 / 80 = 3.15 (approximately) 576 / 252 = 2.28 (approximately)

These ratios also don't form a consistent pattern. However, if we look at the series as a whole, we can see that each number is a perfect square multiplied by its position in the series:

12 = 1 * (4^2) 80 = 2 * (6^2) 252 = 3 * (7^2) 576 = 4 * (8^2)

Following this pattern, the next number in the series should be 5 * (9^2), which equals 405.

This problem has been solved

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