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 1

f(1) = 5 and f(n) = f(n - 1) + 3; n 1

f(1) = 3 and f(n) = f(n - 1) + 5n; n 1

f(1) = 5 and f(n) = f(n - 1) + 3n; n 1

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 > 1

 f(1) = 5 and f(n) = f(n - 1) + 3; n > 1

 f(1) = 3 and f(n) = f(n - 1) + 5n; n > 1

 f(1) = 5 and f(n) = f(n - 1) + 3n; n > 1

anonymous · Answer

Since the first term is 3, you can eliminate the choices with $f(1)=5$.

anonymous · Answer

Beyond that, you can choose between the others by plugging in for $n$.

According to the definition of this recursion, the next term will add 5 to the previous term.

So if the first term is $f(1)=3$, then the second term must be $f(2)=3+5=8$, or $f(2)=f(1)+5$. What does that tell you?

anonymous · Answer

that for every F(x), its 3+5+whatever the last number is

anonymous · Answer

Not quite, that would mean the sequence is defined by
$$\begin{cases}f(1)=3\f(n)=f(n-1)+8\end{cases}$$
which is not one of the options.

anonymous · Answer

ohh, so just plus 5 every time then?

anonymous · Answer

@SithsAndGiggles

anonymous · Answer

@nikosis01 can you help real quick?

nikosis01 · Answer

sure

anonymous · Answer

@KryoWolf yes just plus 5

anonymous · Answer

ok thanks sith

anonymous · Answer

so if f(2)=3+5=8, then f(3)=8+5=13

anonymous · Answer

so C @SithsAndGiggles

anonymous · Answer

No, not C. C says
$$f(n)=f(n-1)+5n$$
But that would mean
$$f(2)=f(2-1)+5(2)=f(1)+10=13\not=8$$

anonymous · Answer

ok, so its A

anonymous · Answer

yes