Answer:
The correct option is 1.
Step-by-step explanation:
It is given that the first term of a geometric sequence is 16 the fifth term of the sequence is 150.06.
[tex]a_1=16[/tex]
[tex]a_5=150.06[/tex]
The nth term of a geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex] .... (1)
The fifth term of the sequence is
[tex]a_5=a_1r^{5-1}[/tex]
Substitute [tex]a_1=16[/tex] and [tex]a_5=150.06[/tex].
[tex]150.06=16r^{4}[/tex]
Divide both sides by 16.
[tex]9.37875=r^{4}[/tex]
[tex](9.37875)^{\frac{1}{4}}=r[/tex]
[tex]r\approx 1.75[/tex]
Substitute n=17, [tex]a_1=16[/tex] and [tex]r=1.75[/tex] to find the 17th term.
[tex]a_{17}=16(1.75)^{17-1}[/tex]
[tex]a_{17}=123802.31384[/tex]
[tex]a_{17}\approx 123802.31[/tex]
Therefore the correct option is 1.
