Provide an appropriate response.
-Determine the general term of the sequence $6 , - 15 , \frac { 75 } { 2 } , - \frac { 375 } { 4 } , \ldots$
A) $a _ { n } = 6 \left( - \frac { 5 } { 2 } \right) ^ { n - 1 }$
B) $a _ { n } = \frac { 5 } { 2 } ( 6 ) ^ { n - 1 }$
C) $a _ { n } = - 6 \left( \frac { 5 } { 2 } \right) ^ { n - 1 }$
D) $a _ { n } = 6 \left( - \frac { 5 } { 2 } \right) ^ { n }$

Question

Quizplus · Accepted Answer

The sequence can be seen as a geometric sequence where each term is multiplied by $-\frac{5}{2}$ to get the next term. The first term is 6, so the general term is $a_n = 6 \left( -\frac{5}{2} \right)^{n-1}$.

Provide an Appropriate Response 6,−15,752,−3754,…6 , - 15 , \frac { 75 } { 2 } , - \frac { 375 } { 4 } , \ldots6,−15,275​,−4375​,…

Provide an Appropriate Response $6 , - 15 , \frac { 75 } { 2 } , - \frac { 375 } { 4 } , \ldots$