Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-$$\mathrm { a } = 2 ; \mathrm { r } = 3$$
A) $a _ { 5 } = 162 ; a _ { n } = 2 \cdot ( 3 ) ^ { n - 1 }$
B) $\mathrm { a } _ { 5 } = 486 ; \mathrm { a } _ { \mathrm { n } } = 2 \cdot ( 3 ) ^ { \mathrm { n } }$
C) $a _ { 5 } = 162 ; a _ { n } = 2 \cdot ( 3 ) ^ { n }$
D) $a _ { 5 } = 486 ; a _ { n } = 2 \cdot ( 3 ) ^ { n - 1 }$

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, $n = 5$, so $a_5 = 2 \cdot 3^{5-1} = 2 \cdot 3^4 = 2 \cdot 81 = 162$. The nth term formula is correctly given as $a_n = 2 \cdot (3)^{n-1}$.

Find the Fifth Term and the Nth Term of the Geometric