Answer:
Explanation:
To write a recursive sequence that represents the sequence defined by the explicit formula an = 10 + 4(n + 1), we need to find a recursive formula that relates each term in the sequence to the previous term.
We can start by noticing that the explicit formula for the first term (a1) is:
a1 = 10 + 4(1 + 1) = 18
To find the next term (a2), we substitute n = 2 into the explicit formula:
a2 = 10 + 4(2 + 1) = 22
To find the third term (a3), we substitute n = 3 into the explicit formula:
a3 = 10 + 4(3 + 1) = 26
We can see that each term in the sequence is obtained by adding 4 to the previous term. Therefore, we can define the recursive formula as follows:
a1 = 18
an+1 = an + 4
This recursive formula states that the first term of the sequence is 18, and that each subsequent term is obtained by adding 4 to the previous term. This recursive formula generates the same sequence as the original explicit formula, and can be used to calculate any term in the sequence.