Question

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

Answer 1

Answer:

Required value of f(0) = 4 and common difference of given sequence is $\frac{-2}{3}$

Solution:

Given sequence rule for arithmetic sequence is  $\mathrm{f}(\mathrm{x})=4-\left(\frac{2}{3}\right) x$

We need to determine f(0) and common difference

Calculating f(0).

Substituting x = 0 in given sequence rule  we get

$\begin{array}{l}{f(0)=4-\left(\frac{2}{3}\right) 0} \\ {=4-0=4}\end{array}$

Calculating common difference  

Let’s first calculate f(1) and f(2).

Substituting x = 1 in given sequence rule  

$\begin{array}{l}{\mathrm{f}(1)=4-\left(\frac{2}{3}\right) 1} \\ {=4-\left(\frac{2}{3}\right)=\frac{10}{3}}\end{array}$

$\mathrm{f}(2)=4-\left(\frac{2}{3}\right) 2=4-\left(\frac{4}{3}\right)=\frac{8}{3}$

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

$\text { Common difference }=\mathrm{f}(2)-\mathrm{f}(1)=\left(\frac{8}{3}\right)-\left(\frac{10}{3}\right)=\frac{-2}{3}$

Hence required value of f(0) = 4 and common difference of given sequence is $\frac{-2}{3}$