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Shalnov [3]
3 years ago
15

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)=
Mathematics
1 answer:
maria [59]3 years ago
7 0

<u>Answer: </u>

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

<u>Solution: </u>

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) = \frac{f(1)}{f(6)}  

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

so f(0) = \frac{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))

\frac{f(2)}{f(1)} = 6

And \frac{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.

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A) (3)² = 3 × 3 and 10(8)² = 10 × 8 × 8

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