Write the first five terms of the sequence $a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }$ . Assume that n begins with 1.
A) $a _ { 1 } = - \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = - \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = - \frac { 1 } { 26 }$
B) $a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }$
C) $a _ { 1 } = - 1 , a _ { 2 } = \frac { 1 } { 4 } , a _ { 3 } = - \frac { 1 } { 9 } , a _ { 4 } = \frac { 1 } { 16 } , a _ { 5 } = - \frac { 1 } { 25 }$
D) $a _ { 1 } = \frac { 1 } { 2 } , a _ { 2 } = - \frac { 1 } { 5 } , a _ { 3 } = \frac { 1 } { 10 } , a _ { 4 } = - \frac { 1 } { 17 } , a _ { 5 } = \frac { 1 } { 26 }$
E) $a _ { 1 } = 1 , a _ { 2 } = - \frac { 1 } { 4 } , a _ { 3 } = \frac { 1 } { 9 } , a _ { 4 } = - \frac { 1 } { 16 } , a _ { 5 } = \frac { 1 } { 25 }$

Question

Quizplus · Accepted Answer

Plug in n = 1, 2, 3, 4, 5 to the expression of $a_n$ given. We get $-\frac{1}{2}, \frac{1}{5}, -\frac{1}{10}, \frac{1}{17}, -\frac{1}{26}$ respectively. Therefore, the first five terms of the sequence are $-\frac{1}{2}, \frac{1}{5}, -\frac{1}{10}, \frac{1}{17}, -\frac{1}{26}$. Thus choice A is correct.

Write the First Five Terms of the Sequence an=(−1)n+4n2+1a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }an​=n2+1(−1)n+4​

Write the First Five Terms of the Sequence $a _ { n } = \frac { ( - 1 ) ^ { n + 4 } } { n ^ { 2 } + 1 }$