Given the general n th term of the sequence,
[tex]f(n)=-8+3(n-1)[/tex]
For n = 1,
[tex]\begin{gathered} f(1)=-8+3(1-1) \\ =-8 \end{gathered}[/tex]
Therefore, the first statement is true.
Now for n = 2,
[tex]\begin{gathered} f(2)=-8+3(2-1) \\ =-8+3 \\ =-5 \end{gathered}[/tex]
Therefore, the first two terms of the sequence is -8 and -5.
So, the common difference is,
[tex]-5-(-8)=-5+8=3[/tex]
Therefore, the common difference is 3.
So, the second statement is true.
Now fifth term is for n = 5.
Therefore,
[tex]\begin{gathered} f(5)=-8+3(5-1) \\ =-8+(3\times4) \\ =-8+12 \\ =4 \end{gathered}[/tex]
Therefore the fifth term is 4 but not 7.
Hence, the third statement is false.
