To find the recursive formula for the arithmetic sequence 7, 5, 3, 1, −1, we need to identify two components:
- The first term of the sequence.
- The common difference between successive terms.
The first term \( a_1 \) is 7.
To find the common difference \( d \), we can subtract the second term from the first term:
\[ d = 5 - 7 = -2 \]
Now, we can write the recursive formula.
The recursive formula format is:
- \( a_1 = 7 \)
- \( a_n = a_{n-1} + d \)
Since our common difference is -2, we have:
- \( a_n = a_{n-1} - 2 \)
Therefore, the correct answer from the options provided is:
a1=7, an=an−1−2
So, the complete recursive formula is:
- \( a_1 = 7 \)
- \( a_n = a_{n-1} - 2 \) for \( n > 1 \)