A formula for the term of a sequence

Question

A seemingly simple but a challenging quiz, find the nth term in 1,6,30,120.....

I am thinking is a quadratic due to the constant difference but n th term is needed not a recursive one - I got confused

Answer 1

It seems to me like $$ a_1=1$$

$$ a_2=1\times 6 =6$$

$$ a_3 = 6\times 5 =30$$

$$ a_4 =30\times 4 =120$$

$$ a_5 =120\times 3 = 360$$

Thus $$a_1=1, a_2=6$$

And for $n\ge 3$,

$$ a_{n+1} = (8-n)a_n $$