THe explict rule for a sequence is given.
an=4n-1
What is the recursive for the sequence?
I got a1=3 ; an=an-1+4
ao=-1; an=a(n-1)+4
To find the recursive formula for a sequence, we need to express each term in terms of the previous term(s).
The explicit formula for the sequence is given as:
an = 4n - 1
Based on this explicit formula, we can determine the recursive formula by expressing each term as a function of the previous term:
To find the recursive formula, we can express a term (an) as a function of the previous term (an-1).
For the sequence an = 4n - 1, we can rewrite it in terms of the previous term (an-1) as:
an = a(n-1) + 4
Therefore, the recursive formula for the given sequence is:
a1 = 3 (given initial term)
an = an-1 + 4
Hence, your recursive formula: a1 = 3 ; an = an-1 + 4
To find the recursive rule for the sequence with the explicit rule an = 4n - 1, you can use the relationship between the terms.
The recursive rule represents how each term in the sequence is related to the previous term(s). In this case, you can see that each term is obtained by adding 4 to the previous term.
So, the recursive rule for the sequence is:
a1 = 3 (the given starting term)
an = an-1 + 4 (each term is obtained by adding 4 to the previous term)
Therefore, the recursive rule for this sequence is:
a1 = 3
an = an-1 + 4