Answer: The common ratio is 2.
[tex]f(1)=16[/tex]
[tex]f(5)=256[/tex]
Step-by-step explanation:
The given geometric sequence. is
16, 32, 64, 128, ...
Also, The common ratio (r)=[tex]\frac{a_{n+1}}{a_n}=\frac{a_2}{a_1}=\frac{32}{16}=2[/tex]
Hence, the common ratio (r)= 2
Given that the sequence is represented by the function f.
Then [tex]f(n)=a_1r^{n-1}[/tex]
Then, the first term of G.P. =[tex]f(1)=16[/tex]
For n=5, [tex]f(5)=16(2)^{5-1}=16(2)^4=16\times16=256[/tex]
Hence, f(5)=256
