Write an expression for the nth term of the geometric sequence.Then find the indicated term.? $$a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10$$ ?
A) $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$
B) $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$
C) $a _ { n } = 4 \left( \frac { 1 } { 6 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$
D) $a _ { n } = 6 \left( \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 1 } { 2,519,424 }$
E) $a _ { n } = \left( \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 1 } { 2,519,424 }$

Question

Quizplus · Accepted Answer

The formula for the nth term of a geometric sequence is $a_n = a_1 \cdot r^{n-1}$, where $a_1$ is the first term and $r$ is the common ratio. Given $a_1 = 4$ and $r = \frac{1}{6}$, the formula becomes $a_n = 4 \left( \frac{1}{6} \right)^{n-1}$. For $n = 10$, $a_{10} = 4 \left( \frac{1}{6} \right)^{9}$, which simplifies to $\frac{1}{2,519,424}$.

Write an Expression for the Nth Term of the Geometric a1=4,r=16,n=10a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10a1​=4,r=61​,n=10

Write an Expression for the Nth Term of the Geometric $a _ { 1 } = 4 , r = \frac { 1 } { 6 } , n = 10$