Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-$$\mathrm { a } = - 8 ; \mathrm { r } = - 5$$
A) $\mathrm { a } _ { 5 } = 1,000 ; \mathrm { a } _ { \mathrm { n } } = - 8 \cdot ( - 5 ) ^ { \mathrm { n } }$
B) $\mathrm { a } _ { 5 } = - 5,000 ; \mathrm { a } _ { \mathrm { n } } = - 8 \cdot ( - 5 ) ^ { \mathrm { n } }$
C) $a _ { 5 } = - 5,000 ; a _ { n } = - 8 \cdot ( - 5 ) ^ { n - 1 }$
D) $a _ { 5 } = 1,000 ; a _ { n } = - 8 \cdot ( - 5 ) ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The fifth term of a geometric sequence is found using the formula $a_n = a \cdot r^{n-1}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the term number. For the fifth term ($n=5$), $a_5 = -8 \cdot (-5)^{5-1} = -8 \cdot (-5)^4 = -8 \cdot 625 = -5000$. The nth term formula is correctly represented as $a_n = -8 \cdot (-5)^{n-1}$.

Find the Fifth Term and the Nth Term of the Geometric