Find the fifth term of the sequence that has the given nth term. $$a _ { n } = \frac { ( n + 2 ) ! } { n ! }$$
A) $42$
B) $30$
C) $12$
D) $20$
E) $6$

Question

Quizplus · Accepted Answer

The nth term of the sequence is given by $a_n = \frac{(n+2)!}{n!}$. For the fifth term, substitute $n = 5$:  $$a_5 = \frac{(5+2)!}{5!} = \frac{7!}{5!} = \frac{7 \times 6 \times 5!}{5!} = 7 \times 6 = 42.$$

Find the Fifth Term of the Sequence That Has the Given