Question

Which represents the recursive formula for the arithmetic sequence an= 7 - 3(n-1)?

a) a3 = a2 * 3
b) a2 = a1 - 3
c) a2 = a1 + 3
d) a3 = a2 - 7

Answer 1

The recursive formula for the arithmetic sequence a_n = 7 - 3(n-1) is a_n = a_(n-1) - 3 for n > 1, starting with a_1 = 7. The correct option is b) a_2 = a_1 - 3.

Step-by-step explanation:

The given arithmetic sequence can be represented as an = 7 - 3(n-1). To determine the recursive formula, we need to express the nth term using the (n-1)th term. Observing the given expression, we can see that each term is less than the previous term by 3. Thus, starting from the first term a1, each subsequent term is found by subtracting 3 from the preceding term. The recursive formula is then given by an = an-1 - 3, for n > 1, with the first term a1 equal to 7.

The correct option based on this explanation is:
b) a2 = a1 - 3,

since it represents the recursive relationship between two consecutive terms in the sequence.