I have a sequence. It begins:
1
101
10101
1010101
101010101
etc
As it’s populated entirely with 1s and 0s it is not entirely clear whether these are decimal numbers, or binary numbers, or some other base entirely.
Construct a formula to give the nth term, which works no matter what base we are working in.
***EDIT*** You are looking for a simple formula where you plug in the value of n and get the nth term, no recursive formulae or finite sums required.