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given the arithmetic or geometric sequences, identify f(0) and the common difference/ratio. f(x) =f(x-1) - 14;f(2)=5

User Flat
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1 Answer

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Answer:

For given sequence f(0) is 33 and common difference is -14

Solution:

Given sequence rule of arithmetic sequence is f(x) = f(x-1) – 14

Also given that f(2) = 5.

We need to evaluate f(0)

Lets first calculate f(1) from f(2)

Putting x = 2 in given sequence rule , we get

f(2) = f(2-1) – 14

f(2) = f(1) – 14

On rearranging terms, we get

f(1) = f(2) + 14

= 5 + 14 = 19

Substituting x = 1 in sequence rule

f(1) =f(1-1) – 14=f(0) - 14

substituting calculated value of f(1)

19 = f(0) – 14

f(0) = 19 + 14 = 33.

Common difference of the sequence

f(2) –f(1) = 5 – 19 = -14

hence for given sequence f(0) is 33 and common difference is -14.

User Rooz
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