Answer:
Option c is correct.
The sequence is, 2, -3 , -8 , -13, -18, .....
Step-by-step explanation:
Given the following as;
f(1) = 2
The recursive function is;[tex]f(n) = f(n-1) -5[/tex] ......[1]
to find the sequence defined by the recursive function;
Put n=2 in [1];
[tex]f(2) = f(2-1) -5[/tex]
[tex]f(2) = f(1) -5[/tex]
Substitute the value of f(1) = 2 we have;
[tex]f(2) = 2-5 = -3[/tex]
Similarly, put n =3
[tex]f(3) = f(3-1) -5[/tex]
[tex]f(3) = f(2) -5[/tex]
Substitute the value of f(2) = -3 we have;
[tex]f(3) = -3-5 = -8[/tex]
for n = 4 we have;
[tex]f(4) = f(4-1) -5[/tex]
[tex]f(4) = f(3) -5[/tex]
Substitute the value of f(3) = -8 we have;
[tex]f(4) = -8-5 = -13[/tex] and so on .......
Therefore, we get the sequence defined by the recursive formula is,
2, -3 , -8 , -13, -18, .........
