1,1/2,1/6,1/24,1/120 Write an expression for the n'th term of the sequence. (There is more than one correct answer.)

Consider the ratios between adjacent terms of the given sequence:
1/2 : 1 = 1/2,  1/6 : 1/2 = 1/3,  1/24 : 1/6 = 1/4, 1/120 : 1/24 = 1/5.
We see that the n -th term of the sequence may be obtained from the (n-1)-th term by multiplying by 1/n.
Therefore the n-th term may be predicted to be equal to
a_n = 1/(n(n-1)(n-2)...) = 1/(n!)