Find The $1000 ^ { \mathrm { th } }$ Term of the Sequence

Find the $1000 ^ { \mathrm { th } }$ term of the sequence $a _ { n } = ( - 1 ) ^ { n } \frac { n + 2 } { n }$

A) $a _ { 1000 } = - \frac { 501 } { 500 }$

B) $a _ { 1000 } = \frac { 251 } { 250 }$

C) $a _ { 1000 } = \frac { 126 } { 125 }$

D) $a_{1000}= - \frac { 126 } { 125 }$

E) $a _ { 1000 } = \frac { 501 } { 500 }$