Write a formula for the nth term of the geometric sequence.
-$$\frac { 64 } { 5 } , 8,5 , \frac { 25 } { 8 }$$
A) $a _ { n } = \frac { 64 } { 5 } \left( \frac { 5 } { 8 } \right) ^ { n }$
B) $a _ { n } = 64 \left( \frac { 1 } { 8 } \right) ^ { n - 1 }$
C) $a _ { n } = 8 ^ { n }$
D) $a _ { n } = \frac { 64 } { 5 } \left( \frac { 5 } { 8 } \right) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The common ratio (r) of the sequence can be found by dividing any term by its preceding term, e.g., $8 / (\frac{64}{5}) = \frac{5}{8}$. The first term (a1) is $\frac{64}{5}$. Thus, the nth term formula for a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$, which gives $a_n = \frac{64}{5} \cdot (\frac{5}{8})^{n-1}$.

Write a Formula for the Nth Term of the Geometric 645,8,5,258\frac { 64 } { 5 } , 8,5 , \frac { 25 } { 8 }564​,8,5,825​

Write a Formula for the Nth Term of the Geometric $\frac { 64 } { 5 } , 8,5 , \frac { 25 } { 8 }$