Question

The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).
309, comma, 303, comma, 297, comma, point, point, .
309,303,297,...
Find the 31st term.
Find the 31st term.

Answer 1

To find the 31st term of the sequence with the first three terms given as 309, 303, and 297, we first need to identify the pattern of the sequence.

1. **Identify the pattern:**
- The first term is 309.
- The second term is 303, which is 309 - 6.
- The third term is 297, which is 303 - 6.

From this, we can see that the sequence is decreasing by 6 each time.

2. **General formula:**
The \( n \)-th term of an arithmetic sequence can be found using the formula:
\[
a_n = a_1 + (n-1) \cdot d
\]
where \( a_1 \) is the first term, \( d \) is the common difference, and \( n \) is the term number.

Here:
- \( a_1 = 309 \)
- \( d = -6 \) (since the sequence is decreasing by 6)

3. **Calculate the 31st term:**
We want to find \( a_{31} \):
\[
a_{31} = 309 + (31 - 1) \cdot (-6)
\]
\[
a_{31} = 309 + 30 \cdot (-6)
\]
\[
a_{31} = 309 - 180
\]
\[
a_{31} = 129
\]

Thus, the 31st term of the sequence is \( \boxed{129} \).