Question

The first term in an arithmetic sequence is 5. The third term in the sequence is -1. The tenth term in the sequence is -22.

Xavier said that the recursive formula for this sequence could be described as, "to find the next term of the sequence, add -3 to the previous term." Do you agree or disagree that this statement is equivalent to the explicit formula from Part A? Explain.

Answer 1

Xavier's recursive formula is not equivalent to the explicit formula for the arithmetic sequence.

Step-by-step explanation:

The recursive formula given by Xavier, "to find the next term of the sequence, add -3 to the previous term," is not equivalent to the explicit formula for this sequence.

The explicit formula for an arithmetic sequence is given by: an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, and d is the common difference.

In this sequence, the common difference is -3, but Xavier's recursive formula states to add -3 to the previous term, which would be an-1, not an. Therefore, Xavier's formula is not equivalent to the explicit formula.