Question

I recursive rule for the arrhythmic sequence is a one equals 418 equals eight and-1-3 what is the explicit rule for the sequence answer the simplified answer in the box

Answer 1

The explicit rule for the arithmetic sequence with the recursive formula an = an-1 + 8 and a1 = 4 is an = 8n - 4.

Step-by-step explanation:

The student is asking for the explicit rule of an arithmetic sequence based on the given recursive formula. For an arithmetic sequence defined recursively by a1 = 4, an = an-1 + 8, the explicit, or general, form of the sequence can be found using the formula an = a1 + (n-1)d, where a1 is the first term and d is the common difference.

In this case, the first term a1 is 4, and the common difference d is 8. Plugging these values into the formula, we get an = 4 + (n-1)8, which simplifies to an = 8n - 4 as the explicit rule for the sequence.