An arithmetic sequence is represented by the recursive formula a(n)=a(n-1)+8. If the first term in the sequence is 4, write the explicit formula.
To find the explicit formula for an arithmetic sequence, we need to find the common difference, which is the value being added to each term to obtain the next term.
In this case, the common difference is 8, as given by the recursive formula a(n) = a(n-1) + 8.
The explicit formula for an arithmetic sequence is of the form a(n) = a₁ + d(n-1), where a₁ is the first term and d is the common difference.
Given that the first term a₁ is 4 and the common difference d is 8, the explicit formula for this arithmetic sequence is:
a(n) = 4 + 8(n-1)