Question

a sequence is defined recursively by the equation an=an-1+3 where a1 =0. Which of the following defines this sequence in function notation ?a. f(n)=3nb. f(n)= n+3 c. F(n) =3 (n-1)d. f(n) =3(n+1)

Answer 1

Notice that the first term of the sequence is a_1 = 0. Then, for the function notation, we must have:

$f(1)=0$

thus, the only function that meets this criteria is f(n) = 3(n-1)