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

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.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.

if a = 1,   and b = 2, then the answer is 47.99999999. if you round that to the nearest whole number, the answer is 48.