Find the fifth term and the nth term of the geometric sequence whose initial term, a, and common ratio, r, are given.
-$$a = \sqrt { 5 } ; r = \sqrt { 5 }$$
A) $\mathrm { a } _ { 5 } = 25 \sqrt { 5 } , \mathrm { a } _ { \mathrm { n } } = 5 ^ { \mathrm { n } / 2 }$
B) $\mathrm { a } _ { 5 } = 625 \sqrt { 5 } , \mathrm { a } _ { \mathrm { n } } = 5 ^ { \mathrm { n } - 1 / 2 }$
C) $a _ { 5 } = 5 \sqrt { 5 } , a _ { n } = 5 ^ { n / 2 - 1 }$
D) $a _ { 5 } = 3,125 , a _ { n } = 5 ^ { n }$

Question

Quizplus · Accepted Answer

The nth term of a geometric sequence is given by $a_n = a \cdot r^{n-1}$. For $a = \sqrt{5}$ and $r = \sqrt{5}$, the nth term is $a_n = \sqrt{5} \cdot (\sqrt{5})^{n-1} = 5^{1/2} \cdot 5^{(n-1)/2} = 5^{n/2}$. The fifth term, $a_5$, is $5^{5/2} = 5^2 \cdot 5^{1/2} = 25\sqrt{5}$.

Find the Fifth Term and the Nth Term of the Geometric