Write an expression for the n th term of the sequence $4 , \frac { 4 } { 2 } , \frac { 4 } { 6 } , \frac { 4 } { 24 } , \frac { 4 } { 120 } , \ldots$ Assume that n begins with 1.
A) $a _ { n } = 4 + \frac { 1 } { n ! }$
B) $a _ { n } = \frac { 4 } { ( n + 1 ) }$
C) $a _ { n } = \frac { 4 } { n ( n + 1 ) }$
D) $a _ { n } = \frac { 4 } { n ! }$
E) $a _ { n } = 4 + \frac { 1 } { ( n + 1 ) ! }$

Question

Quizplus · Accepted Answer

The given sequence is $4, \frac{4}{2}, \frac{4}{6}, \frac{4}{24}, \frac{4}{120}, \ldots$, where the denominator follows the pattern of factorial numbers starting from $1!$ for $n=1$. Thus, the $n$th term is given by $a_n = \frac{4}{n!}$.

Write an Expression for the N Th Term of the Sequence