36. Kelly's art teacher is modeling a project for art and algebra.The students are going to create a project with blocks in a patteren. Students will use algebra to describe the pattern. A student puts two formulas on the board. Recursive:f(0)=3, f(n)=2*f(n-1)
Explict: f(n)=3*2^n
a. using the recursive formula above,write the first 5 terms of the sequence.
b.You want to know the value of f(30). Is it more efficent to use the recursive or explicit formula? Explain your answer.

Question

36. Kelly's art teacher is modeling a project for art and algebra.The students are going to create a project with blocks in a patteren. Students will use algebra to describe the pattern. A student puts two formulas on the board. Recursive:f(0)=3, f(n)=2*f(n-1)
Explict: f(n)=3*2^n
a. using the recursive formula above,write the first 5 terms of the sequence.
b.You want to know the value of f(30). Is it more efficent to use the recursive or explicit formula? Explain your answer.

mathstudent55 · Answer

a. What is the first term of the sequence? You are told what it is.

mathstudent55 · Answer

a. 
f(0) means the first term.
f(0) = 3 means that the first term is 3.
How do you get the next term?
Each term is 2 times the previous term. That is what f(n) = 2*f(n-1) means.
Since you know the first term is 3, you can find the next 4 terms.

mathstudent55 · Answer

Notice that to find any term in the recursive formula, you must know the immediately previous one.
Now look at part b.
How does the explicit formula work?
If you pick any term you need, let's say the 4th one, then n = 4.
Using the explicit formula, just plug in 4 into it to find the 4th term.
Using the explicit formula, to find any term, you don't need to find the previous term.