Determine the 34th term of the arithmetic sequence 97, 91, 85, . . . .
To find the 34th term of an arithmetic sequence, we can use the formula:
\[ a_n = a_1 + (n-1)d \]
where:
- \( a_n \) is the nth term
- \( a_1 \) is the first term
- \( n \) is the term number
- \( d \) is the common difference between terms
In this case, the first term \( a_1 = 97 \), the common difference \( d = -6 \) (since each term decreases by 6), and we want to find the 34th term, so \( n = 34 \).
Plug these values into the formula:
\[ a_{34} = 97 + (34-1)(-6) \]
\[ a_{34} = 97 + 33(-6) \]
\[ a_{34} = 97 - 198 \]
\[ a_{34} = -101 \]
So, the 34th term of the arithmetic sequence is -101.