Question

An arithmetic sequence has the recursive formula (a_n = a_n-1 - 4) with (a_1 = 5). What is the explicit formula for this sequence?

A. (a_n = 5 + (n-1)(-4))
B. (a_n = 5 + (n-4)(-1))
C. (a_n = (-1) + (n - 5)(-4))
D. (a_n = (-4) + (n-1)5)

Answer 1

The explicit formula for the given arithmetic sequence is an = 5 + (n-1)(-4).

Step-by-step explanation:

An arithmetic sequence with a recursive formula can be converted to an explicit formula. In this case, the recursive formula is an = an-1 - 4, with a1 = 5. To find the explicit formula, we need to express an in terms of n.

To do this, we can observe that each term is subtracted by 4 from the previous term. So, if we start with the given a1 = 5 and continue subtracting 4 for each subsequent term, we can write the explicit formula as an = 5 + (n-1)(-4), which is option A.