Question

Find the recursive formula for the arithmetic sequence 7, 5, 3, 1, -1 ...
a1= 7, an =2an-1
a1= 7, an = an-1 -2
a1= 7, an = -2an-1
a1= 7, an = an-1 +2

Answer 1

To find the recursive formula for the arithmetic sequence 7, 5, 3, 1, -1, we start by recognizing the first term and the common difference.

The first term is:
\[ a_1 = 7 \]

The common difference can be calculated as follows:
- The difference between the second term (5) and the first term (7) is:
\[ 5 - 7 = -2 \]

Continuing this for the next terms:
- The difference between the third term (3) and the second term (5) is:
\[ 3 - 5 = -2 \]

The pattern continues with a common difference of -2.

Therefore, the recursive formula for this arithmetic sequence can be expressed as:
\[ a_n = a_{n-1} - 2 \]
for \( n > 1 \), with the initial condition:
\[ a_1 = 7 \]

Thus, the correct recursive formula from the given options is:
**a1 = 7, an = an-1 - 2**.