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Question

Identify the pattern in the following sequence.

99, 399, 899, 1599, 2499

What is the next number in the sequence?

The correct answer is

3599

Each term is one less than a perfect square of a multiple of ten.

\(99 = 10^2 - 1\), \(399 = 20^2 - 1\), \(899 = 30^2 - 1\), \(1599 = 40^2 - 1\), \(2499 = 50^2 - 1\).

The bases increase as 10, 20, 30, 40, 50, so the next base is 60.

Compute \(60^2 - 1 = 3600 - 1 = 3599\).

This also matches the growing differences 300, 500, 700, 900, then 1100 giving \(2499 + 1100 = 3599\).

Hence the next number is 3599.

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