Answer:
Required value of f(0) = 2 and common ratio of given geometric sequence is 6.
Solution:
Given sequence rule for geometric sequence is f(x) = f(x-1) multiplied by 6 that is,
f(x) =6(f(x-1)) .
Also given that f(1) = 12 .
We need to determine f(0) and common ratio.
Calculating f(0) :
On substituting x = 1 in given sequence rule, we get
f(1) = 6(f(1-1))
f(1) = 6(f(0))
f(0) = [tex]\frac{f(1)}{f(6)}[/tex]
Given that f(1) = 12, substituting in above expression we get
so f(0) = [tex]\frac{12}{6}[/tex] = 2
Calculation common ratio:
On substituting x = 2 in given sequence rule, we get
f(2) = 6(f(2-1))
f(2) = 6(f(1))
[tex]\frac{f(2)}{f(1)}[/tex] = 6
And [tex]\frac{f(2)}{f(1)}[/tex] is nothing but common ratio.
Hence required value of f(0) = 2 and common ratio of given geometric sequence is 6.
