Try each statement to figure out if it holds or not.
[tex]f(n)=-4(n-1)\text{ for all n}\ge2[/tex]
Try n=2, if the statement is true, then f(2) should be -4:
[tex]f(2)=-4(2-1)=-4(1)=-4[/tex]
Try n=3, if the statement is true, then f(3) should be 0:
[tex]f(3)=-4(3-1)=-4(2)=-8\text{ }![/tex]
Therefore, the first statement is false.
Since the sequence is an arithmetic sequence, the first term is equal to -8 and the common difference of its terms is equal to 4, then the explicit rule for the sequence is:
[tex]f(n)=-8+4(n-1)[/tex]
By trying different values of n you can convince yourself that this statement is true.
The tenth term is given by:
[tex]\begin{gathered} f(10)=-8+4(10-1) \\ =-8+4(9) \\ =-8+36 \\ =28 \end{gathered}[/tex]
Therefore, the third statement is true.
