Write an expression for the nth term of the geometric sequence.Then find the indicated term.? $$a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12$$ ?
A) $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$
B) $a _ { n } = 5 \left( - \frac { 1 } { 2 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$
C) $a _ { n } = 6 \left( - \frac { 1 } { 5 } \right) ^ { n + 1 }$ , $\frac { 6 } { 48,828,125 }$
D) $a _ { n } = \left( \frac { 1 } { 2 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$
E) $a _ { n } = 5 \left( - \frac { 1 } { 4 } \right) ^ { n - 1 }$ , $\frac { 6 } { 48,828,125 }$

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, $r$ is the common ratio, and $n$ is the term number. Given $a_1 = 6$ and $r = -\frac{1}{5}$, the formula becomes $a_n = 6 \cdot \left(-\frac{1}{5}\right)^{n-1}$. To find the 12th term, substitute $n = 12$ into the formula, resulting in $a_{12} = 6 \cdot \left(-\frac{1}{5}\right)^{11}$, which simplifies to $\frac{6}{(-5)^{11}}$, not directly given in the options but aligns with the formula in option A.

Write an Expression for the Nth Term of the Geometric a1=6,r=−15,n=12a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12a1​=6,r=−51​,n=12

Write an Expression for the Nth Term of the Geometric $a _ { 1 } = 6 , r = - \frac { 1 } { 5 } , n = 12$