Question

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)=

Answer 1

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) =
`(f(1))/(f(6))`

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

so f(0) =
`(12)/(6)` = 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))

`(f(2))/(f(1))` = 6

And
`(f(2))/(f(1))` is nothing but common ratio.

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