Write the first five terms of the sequence defined recursively.
-$$a _ { 1 } = 6 , a _ { n } = - \frac { 1 } { a _ { n - 1 } }$$
A) $a _ { 1 } = 6 , a _ { 2 } = \frac { 1 } { 6 } , a _ { 3 } = \frac { 1 } { 36 } , a _ { 4 } = \frac { 1 } { 216 } , a _ { 5 } = \frac { 1 } { 1,296 }$
B) $a _ { 1 } = 6 , a _ { 2 } = \frac { 1 } { 6 } , a _ { 3 } = 6 , a _ { 4 } = \frac { 1 } { 6 } , a _ { 5 } = 6$
C) $a _ { 1 } = 6 , a _ { 2 } = - \frac { 1 } { 6 } , a _ { 3 } = \frac { 1 } { 36 } , a _ { 4 } = - \frac { 1 } { 216 } , a _ { 5 } = \frac { 1 } { 1,296 }$
D) $a _ { 1 } = 6 , a _ { 2 } = - \frac { 1 } { 6 } , a _ { 3 } = 6 , a _ { 4 } = - \frac { 1 } { 6 } , a _ { 5 } = 6$

Question

Quizplus · Accepted Answer

The recursive formula $a_n = -\frac{1}{a_{n-1}}$ alternates between positive and negative values. Starting with $a_1 = 6$, the next term is $-\frac{1}{6}$, and applying the formula again results in the negation of the reciprocal, bringing back to 6, and so on, leading to the pattern shown in option D.

Write the First Five Terms of the Sequence Defined Recursively a1=6,an=−1an−1a _ { 1 } = 6 , a _ { n } = - \frac { 1 } { a _ { n - 1 } }a1​=6,an​=−an−1​1​

Write the First Five Terms of the Sequence Defined Recursively $a _ { 1 } = 6 , a _ { n } = - \frac { 1 } { a _ { n - 1 } }$