Question

Given the geometric sequence where a_1 = 3 and r = √2 find a_9

Answer 1

To find n-therm of a geometric sequence, we are going to use the formula $a_{n} =a _{1} r^{n-1}$
where:
$a_{n}$ is the term we are looking for
$a _{1}$ is the first term 
$r$ is the ratio 
$n$ is the position of the number in the sequence 

From the question we now that $a _{1} =3$, $r= \sqrt{2}$, and $n=9$. Lets replace those values into our formula to get:
$a _{9} =3( \sqrt{2} )^{9-1}$
$a_{9} =3 \sqrt{2} ^{8}$
$a_{9} =48$

We can conclude that in our geometric sequence $a_{9} =48$; therefore, the answer is A.