Question

Determine the 34th term of the arithmetic sequence 97, 91, 85...

Answer 1

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 of the sequence,
- \(n\) is the term number,
- \(d\) is the common difference between terms.

In this case, we have:
- \(a_1 = 97\),
- \(d = -6\) (since each term decreases by 6),
- \(n = 34\).

Plugging these values into the formula:

\[a_{34} = 97 + (34 - 1)(-6)\]
\[a_{34} = 97 + 33(-6)\]
\[a_{34} = 97 + (-198)\]
\[a_{34} = -101\]

Therefore, the 34th term of the arithmetic sequence is -101.