Look at this series: 1, 11, 1111, 11111, … What number should come next?

Answer 1

This is a recurrence relation, but hopefully it is missing the third term, otherwise it is a much harder problem.

a₀ = 1

a₁ = 11

a₂ = 111

a₃ = 1111

a₄ = 11111

and so on.

If my suspicion is correct and a₂ was missing, then the recurrence formula follows this format:

a_n = 10^{n +} a_n-1 + 1 = 10 * a_n-1 + 1

So the next number should just be six ones, 111111. However, if my suspicion is wrong, then this is a much harder recurrence problem.