Question

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

Answer 1

f(n+1) = f(n) +5

Step-by-step explanation:

Since f(n) is a term, and f(n+1) is the next term, and since the next term is 5 more than the one before, you expect the formula to look like

f(n+1) = f(n) +5

the other guy is wrong

Answer 2

f(n)=3+(n-1)·5

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.