Choose the one alternative that best completes the statement or answers the question.
Determine whether the sequence is geometric. If so, find the value of r.
-$$\frac { 15 } { t ^ { 4 } } , \frac { 75 } { t ^ { 8 } } , \frac { 375 } { t ^ { 12 } } , \frac { 1,875 } { t ^ { 16 } }$$
A) geometric, $r = \frac { 5 } { t ^ { 4 } }$
B) not geometric
C) geometric, $r = \frac { 15 } { t ^ { 4 } }$
D) geometric, $r = \frac { 1 } { t }$

Question

Quizplus · Accepted Answer

To determine if the sequence is geometric, we check if the ratio between consecutive terms is constant. The ratio between the first and second term is $\frac{75/t^8}{15/t^4} = \frac{75}{15} \cdot \frac{t^4}{t^8} = 5t^{-4} = \frac{5}{t^4}$. This same ratio applies to all consecutive terms, making the sequence geometric with $r = \frac{5}{t^4}$.

Choose the One Alternative That Best Completes the Statement or Answers