Question

Use the function notation to write a recursive formula to represent the sequence: 4, 8, 12, ...

Answer 1

Answer:

The correct answer is f(n) = f(n − 1) + 4

Step-by-step explanation:

Let us consider the sequence: 4, 8, 12, …

Using f(n) = f(n − 1) + 4, we can easily get the sequence.

As the first term is 4 and next term is obtained by adding 4 to the first term.

i.e. 4+4 = 8

     8+4 = 12

     12+4 = 16  and so on.

Since the next term is obtained by adding 4 to the previous term.

So, f(n) = f(n-1) + 4 would be the correct recursive formula for the function of the sequence 4, 8, 12, ....

Verification:

                f(n) = f(n-1) + 4

Putting n=2 in f(n) = f(n-1) + 4 to get the second term of the sequence.

               f(2) = f(2-1) + 4

               f(2) = f(1) + 4

               f(2) = 4 + 4

               f(2) = 8

Putting n=3 in f(n) = f(n-1) + 4 to get the third term of the sequence.

                f(3) = f(3-1) + 4

                f(3) = f(2) + 4

So, adding 4 in f(2)=8 would give us the next term i.e. 12

               f(3) = 8 + 4

                f(3) = 12

Keywords: recursive formula, sequence

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