Given series:

1,4,27,?,3125

We note that 4 is the square of 2, while 27 is the third power of 27 and 3125 is the fifth power of 5:

\(\displaystyle{1}^{{1}},{2}^{{2}},{3}^{{3}},?,{5}^{{5}}\)

Thus we note that the nth term in the sequence appears to be the nth power of n. That is, \(a_{n} = n^n\) when an represents the nth term in the sequence.

This then implies that we expect the fourth term in the sequence to be \(\displaystyle{4}^{{4}}\).

\(\displaystyle{a}{4}={4}^{{4}}={256}\)