How to reconstruct a time-discrete signal
Consider things you know about the sampling theorem:

If it is met, the original signal can always be reconstructed perfectly!
The signal has to be bandlimited for the theorem to be met!

Further, think about the spectral and time domains and their relation to each other:

If a signal is bandlimited in spectral domain, it has to be infinite in time domain.

Then, thinking about the given signal:

The given sampled signal has just zeros before and after the one none-zero value.
It is not periodic.
One can conclude, that in the original signal, there have to be none zero values between all (or at least some) sampling points, otherwise it would not be infinite.

So we have to ask ourselves the question:

Which signal is bandlimited, has zero crossings at regular intervals, a non zero value in the middle and is not periodic?

If you had any lectures on signal theory, the answer should be pretty obvious.