Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-$$\mathrm { a } = 5 ; \mathrm { r } = 3 \pi$$
A) $a _ { 5 } = 405 \pi , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi$
B) $a _ { 5 } = 1,215 \pi ^ { 5 } , a _ { n } = 5 \cdot 3 ^ { n } \pi ^ { n }$
C) $a _ { 5 } = 5 + 12 \pi , a _ { n } = 5 + 3 \pi ( n - 1 )$
D) a5 $= 405 \pi ^ { 4 } , a _ { n } = 5 \cdot 3 ^ { n - 1 } \pi ^ { n - 1 }$

Question

Quizplus · Accepted Answer

The nth term of a geometric sequence is given by $a_n = a \cdot r^{n-1}$. For this sequence, $a = 5$ and $r = 3\pi$. Thus, $a_5 = 5 \cdot (3\pi)^{4} = 405\pi^4$ and $a_n = 5 \cdot (3\pi)^{n-1} = 5 \cdot 3^{n-1} \pi^{n-1}$.

Find the Fifth Term and the Nth Term of the Geometric