Question

Determine the 34th term of the arithmetic sequence 97, 91, 85, . . . .(1 point)
Responses

−9
negative 9

−107
negative 107

−101
negative 101

295

Answer 1

To determine the 34th term of the arithmetic sequence given, we first need to identify the first term and the common difference.

The first term \( a_1 \) is 97.

Next, we calculate the common difference \( d \):
\[
d = 91 - 97 = -6
\]

The formula for the \( n \)-th term of an arithmetic sequence is:
\[
a_n = a_1 + (n - 1) \cdot d
\]

Now, substituting the known values into the formula to find the 34th term (\( n = 34 \)):
\[
a_{34} = 97 + (34 - 1) \cdot (-6)
\]
\[
a_{34} = 97 + 33 \cdot (-6)
\]
\[
a_{34} = 97 - 198
\]
\[
a_{34} = -101
\]

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

The answer is:
\[
\boxed{-101}
\]