Given the arithemtic or geometric sequence, identify f(0) and the common difference/ ratio f(x) = f(x-1) multiplied by 6; f(1)=12 f(0)=

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) =  

Given that f(1) = 12, substituting in above expression we get

so f(0) = = 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))

= 6

And is nothing but common ratio.

Hence required value of f(0) = 2 and common ratio of given geometric sequence is 6.