Respuesta :
Answer:
Required value of f(0) = 4 and common difference of given sequence is [tex]\frac{-2}{3}[/tex]
Solution:
Given sequence rule for arithmetic sequence is [tex]\mathrm{f}(\mathrm{x})=4-\left(\frac{2}{3}\right) x[/tex]
We need to determine f(0) and common difference
Calculating f(0).
Substituting x = 0 in given sequence rule we get
[tex]\begin{array}{l}{f(0)=4-\left(\frac{2}{3}\right) 0} \\ {=4-0=4}\end{array}[/tex]
Calculating common difference
Let’s first calculate f(1) and f(2).
Substituting x = 1 in given sequence rule
[tex]\begin{array}{l}{\mathrm{f}(1)=4-\left(\frac{2}{3}\right) 1} \\ {=4-\left(\frac{2}{3}\right)=\frac{10}{3}}\end{array}[/tex]
[tex]\mathrm{f}(2)=4-\left(\frac{2}{3}\right) 2=4-\left(\frac{4}{3}\right)=\frac{8}{3}[/tex]
Common Difference can be found by subtracting f(1) from f(2)
[tex]\text { Common difference }=\mathrm{f}(2)-\mathrm{f}(1)=\left(\frac{8}{3}\right)-\left(\frac{10}{3}\right)=\frac{-2}{3}[/tex]
Hence required value of f(0) = 4 and common difference of given sequence is [tex]\frac{-2}{3}[/tex]
