ANSWER
[tex]f(1) = - 34[/tex]
[tex]f(n) = f(n - 1) + 13[/tex]
EXPLANATION
The given sequence is;
-34,-21,-8,5,....
The first term of the sequence is
[tex]f(1) = - 34[/tex]
The common difference is
[tex]d = 5 - - 8[/tex]
[tex]d = 5 + 8 = 13[/tex]
The recursive definition is given by;
[tex]f(n) = f(n - 1) + d[/tex]
[tex]f(n) = f(n - 1) + 13[/tex]
for n=2,3,4,...
