Question

Use function notation to write a recursive formula to represent the sequence: 3, 6, 9, …

Answer 1

Answer:

f(n) = f(n - 1) + 3

Step-by-step explanation:

Substitute $n = 1, 2, 3,..$ to get the recursive formula.

OPTION 1: f(n) = f(n - 1) + 3

Substituting n = 1.

f(1) = f(1 - 1) + 3 = 0 + 3 = 3.

Substituting n = 2.

f(2) = f(2 - 1) + 3 = f(1) + 3 = 3 + 3 = 6.

Substituting n = 3.

f(3) = f(3 - 1) + 3 = f(2) + 3 = 6 + 3 = 9.

The numbers match the given sequence. So, we say the above recursive formula represents the sequence.

OPTION 2: f(n) = f(n - 1) + 2

Substituting n = 1

f(1) = f(0) +  2 $\ne$ 3.

So, this is eliminated.

Similarly, OPTION 3 and OPTION 4 can be eliminated as well.