Write four additional terms of the geometric sequence.
-Find the first six terms of the sequence with first term 3 and nth term $a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }$.
A) $3 , - \frac { 2 } { 3 } , \frac { 5 } { 2 } , \frac { 3 } { 5 } , - \frac { 2 } { 3 } , \frac { 5 } { 3 }$
B) $3 , \frac { 2 } { 3 } , \frac { 1 } { 2 } , - 1,2 , \frac { 1 } { 2 }$
C) $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , 3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 }$
D) $3 , \frac { 2 } { 3 } , - \frac { 1 } { 2 } , - 3 , \frac { 4 } { 3 } , \frac { 1 } { 4 }$

Question

Quizplus · Accepted Answer

The given nth term formula $a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }$ is not characteristic of a geometric sequence, but it can be used to find subsequent terms given the first term. Starting with $a_1 = 3$, we can calculate each subsequent term using the formula. The pattern repeats after the third term, showing that the sequence is not geometric but rather follows a specific recursive pattern.

Write Four Additional Terms of the Geometric Sequence an=1−1an−1a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }an​=1−an​−11​

Write Four Additional Terms of the Geometric Sequence $a _ { n } = 1 - \frac { 1 } { a _ { n } - 1 }$