A sequence has its first term equal to 3, and each term of the sequence is obtained by adding 5 to the previous term. If f (n) represents the nth term of the sequence, which of the following recursive functions best defines this sequence? f (1) = 3 and f (n) = f (n - 1) + 5; n > 1f (1) = 5 and f (n) = f (n - 1) + 3; n > 1f (1) = 3 and f (n) = f (n - 1) + 5n; n > 1f (1) = 5 and f (n) = f (n - 1) + 3n; n > 1

f (n) = 3 + (n-1) ·5

Step-by-step explanation:

The first term of the sequence is 3, hence

f (1) = 3.

To find the second term of the the sequence we have to add 5 to f (1), hence

f (2) = 3+5.

To find the third term of the sequence we have to add 5 to f (2), hence

f (3) = 3+5+5 = 3+2·5.

To find the fourth term of the sequence we have to add 5 to f (3), hence

f (3) = 3+2·5+5=3+3·5.

To find the fifth term of the sequence we have to add 5 to f (4), hence

f (3) = 3+3·5+5=3+4·5

...

and so recursively, we have that f (n) = 3 + (n-1) ·5.