Determine the 34th term of the arithmetic sequence 97, 91, 85, . . . .(1 point) Responses −9 negative 9 −101 negative 101 295 295 −107
To find the 34th term of an arithmetic sequence, we can use the formula:
Tn = a + (n-1)d
Where:
Tn = the nth term
a = the first term
n = the term we want to find (34 in this case)
d = common difference
In this sequence:
First term (a) = 97
Common difference (d) = 91 - 97 = -6
Now, plug in the values into the formula:
T34 = 97 + (34-1)(-6)
T34 = 97 + 33(-6)
T34 = 97 - 198
T34 = -101
Therefore, the 34th term of the arithmetic sequence 97, 91, 85, ... is -101.
So the answer is: −101 (negative 101)