Sequence Geometric or Arithmetic Constant Ratio/Difference
-2 4 10 16 22 Arithmetic 6
Recursive Function
f (1) = -2
f (x) = f (x - 1) + 6
What would the explicit function be? I understand the rest just not this it is to confusing.
The constant difference is obviously 6. So, you expect something close to f(n) = 6n.
6*1 = 6, but f(1) = -2, which is 6-8
So, f(n) = 6n-8
WOW that was easier than I thought thanks oobleck! Happy New Year!
To find the explicit function for a given recursive function, we need to express the sequence in terms of a variable, typically denoted as "n."
For the given recursive function:
f(1) = -2
f(x) = f(x-1) + 6
Let's rewrite the first few terms of the sequence using the recursive function:
f(1) = -2
f(2) = f(1) + 6 = -2 + 6 = 4
f(3) = f(2) + 6 = 4 + 6 = 10
f(4) = f(3) + 6 = 10 + 6 = 16
f(5) = f(4) + 6 = 16 + 6 = 22
...and so on.
We notice that the terms of the sequence increase by 6 each time. This implies that the sequence is an arithmetic sequence with a common difference of 6.
Now, to find the explicit function for this arithmetic sequence, we need to determine the initial term or the value of the sequence when n = 1. In this case, it is -2.
The explicit function for an arithmetic sequence is given by:
f(n) = a + (n-1)d,
where:
- f(n) represents the value of the sequence at position n,
- a represents the initial term,
- n represents the position in the sequence,
- d represents the common difference.
For our sequence, the explicit function is:
f(n) = -2 + (n - 1)6.
Now, you can use this explicit function to find the value of any term in the sequence by substituting the desired value of n.