Question

Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, -1,.. (1 point)
0 a1 = 7, an = 2an-1
0 a1 = 7, an = -2an-1
a1 = 7, an = an- 1 + 2
• a1 = 7, an = an-1 - 2

Answer 1

To find the recursive formula for the given arithmetic sequence \(7, 5, 3, 1, -1, \ldots\), we first identify the pattern in the sequence.

The first term \(a_1 = 7\), and each subsequent term decreases by \(2\):

- \(a_2 = a_1 - 2 = 7 - 2 = 5\)
- \(a_3 = a_2 - 2 = 5 - 2 = 3\)
- \(a_4 = a_3 - 2 = 3 - 2 = 1\)
- \(a_5 = a_4 - 2 = 1 - 2 = -1\)

This indicates that the recursive relationship for the sequence can be expressed as:

\(a_1 = 7\)
\(a_n = a_{n-1} - 2\) for \(n \geq 2\)

Thus, the correct option is:

**a1 = 7, an = an-1 - 2**.