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

Answer 1

The common difference in this arithmetic sequence is -6.

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

a_n = a_1 + (n-1)d

where:
a_n = the nth term
a_1 = the first term
d = the common difference
n = the term number

Plugging in the given values:
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.