To find n-therm of a geometric sequence, we are going to use the formula [tex]a_{n} =a _{1} r^{n-1} [/tex] where: [tex]a_{n} [/tex] is the term we are looking for [tex]a _{1} [/tex] is the first term [tex]r[/tex] is the ratio [tex]n[/tex] is the position of the number in the sequence
From the question we now that [tex]a _{1} =3[/tex], [tex]r= \sqrt{2} [/tex], and [tex]n=9[/tex]. Lets replace those values into our formula to get: [tex]a _{9} =3( \sqrt{2} )^{9-1} [/tex] [tex]a_{9} =3 \sqrt{2} ^{8} [/tex] [tex]a_{9} =48[/tex]
We can conclude that in our geometric sequence [tex]a_{9} =48[/tex]; therefore, the answer is A.
