Question

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

Answer 1

To find the 34th term of the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:

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

In this case, the first term (a_1) is 97, the common difference (d) is -6 (since each term decreases by 6), and we want to find the 34th term (n=34).

Plugging in these values into the formula, we get:

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 97, 91, 85, ... is -101.