Question

An arithmetic sequence is represented by the recursive formula A(n) = A(n-1) + 8. The first term in the sequence is 4, write the explicit formula.

Answer 1

The explicit formula for the arithmetic sequence with the given recursive formula A(n) = A(n-1) + 8 and first term 4 is A(n) = 8n - 4.

Step-by-step explanation:

The student is looking to find the explicit formula for an arithmetic sequence described by the recursive formula A(n) = A(n-1) + 8, where the first term A(1) is 4.

The explicit formula of an arithmetic sequence can be given by A(n) = A(1) + (n - 1)d, where A(1) is the first term and d is the common difference of the sequence. Here, the common difference is 8, as indicated by the recursive formula. Therefore, the explicit formula for this arithmetic sequence is A(n) = 4 + (n - 1)×8, which simplifies to A(n) = 4 + 8n - 8 = 8n - 4.