Find The $n ^ { \text {th } }$ Term of the Sequence Whose First Several Terms Are

Multiple Choice

Find the $n ^ { \text {th } }$ term of the sequence whose first several terms are $\frac { 1 } { 4 } , - \frac { 1 } { 9 } , \frac { 1 } { 16 } , - \frac { 1 } { 25 } , \ldots$

A) $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { n ^ { 2 } }$

B) $a _ { n } = \frac { ( - 1 ) ^ { n + 1 } } { ( n + 1 ) ^ { 2 } }$

C) $a _ { \mathrm { n } } = \frac { ( n + 1 ) ^ { n } } { 4 ^ { 2 } }$

D) $a _ { n } = \frac { ( 1 ) ^ { n } } { ( 2 n ) ^ { 2 } }$

E) none of these