Which function is correctly described by the recursive notation g(1)=3
, g(n−1)+3
for n>1
?(1 point)
Responses
g(n)=3n+1
g of n is equal to 3 n plus 1
g(n)=2n−1
g of n is equal to 2 n minus 1
g(n)=3n
g of n is equal to 3 n
g(n)=n+2
The correct function described by the recursive notation is:
g(n) = 2n - 1
The function that is correctly described by the recursive notation is g(n) = 3n.
The correct function described by the recursive notation is g(n) = 3n - 2.
To understand how to get this answer, let's break down the recursive notation:
1. The base case is g(1) = 3. This means that when n is equal to 1, the value of g(n) is 3.
2. The recursive case is g(n-1) + 3. This means that for any value of n greater than 1, the value of g(n) is obtained by taking the value of g(n-1) and adding 3 to it.
We can apply this recursive rule to find g(2), g(3), g(4), and so on:
For g(2):
g(2) = g(2-1) + 3
= g(1) + 3 (using the recursive case)
= 3 + 3 (substituting g(1) with 3)
= 6
For g(3):
g(3) = g(3-1) + 3
= g(2) + 3 (using the recursive case)
= 6 + 3 (substituting g(2) with 6)
= 9
For g(4):
g(4) = g(4-1) + 3
= g(3) + 3 (using the recursive case)
= 9 + 3 (substituting g(3) with 9)
= 12
Following this pattern, we can see that g(n) is equal to 3n - 2.
So, the correct option is g(n) = 3n - 2.