Question

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

a2 = a1 +3
a3 = a₂ - 7
a3 = a2-3
a2 = a₁ - 3

Answer 1

Explanation:

The correct answer is a3 = a2 - 3.

To find the recursive formula for an arithmetic sequence, you need to determine the common difference (d) between consecutive terms. In this case, the first term is 7, and each subsequent term is 3 less than the previous term, so the common difference is -3.

The recursive formula for an arithmetic sequence with a first term a1 and common difference d is:

a1 = a1

a2 = a1 + d

a3 = a2 + d

a4 = a3 + d

and so on.

Substituting the values of a1 and d from the given sequence, we get:

a1 = 7

a2 = a1 + (-3) = 4

a3 = a2 + (-3) = 1

So the recursive formula for the given sequence is a_n = a_n-1 - 3.