Answer
The $n^{th}$ term of the sequence is given by the formula:
$a_n =\sqrt 2 \ (\sqrt 2)^{n-1}$
and
$a_5= 4 \sqrt 2$
Work Step by Step
We are given: $a_{1}=\sqrt 2 ; \ r=\sqrt 2$
The $n^{th}$ term of the sequence is given by the formula:
$a_n=a_1r^{n-1}$
$a_n =\sqrt 2 \ (\sqrt 2)^{n-1}$
Now, the 5th term can be computed by substituting $5$ for $n$:
$a_5=\sqrt 2 \ (\sqrt 2)^{5-1}=\ \sqrt 2 \times (\sqrt 2)^{4}= 4 \sqrt 2$
