Question

Given f(n) is a geometric sequence where f(3)=32 and f(9)=72, find f(16).

Answer 1

Answer:

f(16)=162

Step-by-step explanation:

-In a geometric sequence, the quotient between any tow consecutive numbers is called the common ratio,r:

$r=\frac{a_n}{a_{n-1}}$

Given that f(3)=32 and f(9)=72, we can find the common ratio as below:

$r=\frac{a_n}{a_{n-1}}\\\\\therefore \frac{f(9)}{f(3)}=r^6\\\\\frac{72}{32}=r^6\\\\r^6=2.25\\\\r=2.25^{1/6}$

#We substitute and use the same formula to find the nth term:

$a_n=ar^{n-1}$

let f(3) be a(the first term):

$a_n=ar^{n-1}\\\\a_{16}=32(2.25^{1/6})^{16-3-1}\\\\a_{16}=32(2.25^{1/6})^{12}\\\\\\=162$

Hence, f(16)=162