Given the arithemtic or geometric sequence, identify f(0) and the common difference ratio f(x) = 4-2/3x

Required value of f(0) = 4 and common difference of given sequence is

Solution:

Given sequence rule for arithmetic sequence is  

We need to determine f(0) and common difference

Calculating f(0).

Substituting x = 0 in given sequence rule  we get

Calculating common difference  

Let’s first calculate f(1) and f(2).

Substituting x = 1 in given sequence rule  

Common Difference can be found by subtracting f(1) from f(2)

Hence required value of f(0) = 4 and common difference of given sequence is

the formula of a slope:

we have the points (-2, 7) and (2, 3). substitute: