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

Question

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

Quizplus · Accepted Answer

The sequence is given by $a_n = (-1)^n \frac{n+2}{n}$. For $n = 1000$, $a_{1000} = (-1)^{1000} \frac{1000+2}{1000} = 1 \times \frac{1002}{1000} = \frac{501}{500}$.

Find The 1000th1000 ^ { \mathrm { th } }1000th Term of the Sequence

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