determine the 34th term of the arithmetic sequence 97, 91,85
To find the 34th term of an arithmetic sequence, we need to 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
d is the common difference
n is the term number
In this case, the first term (a_1) is 97, the common difference (d) is -6 (because we are subtracting 6 to get to the next term), and we want to find the 34th term (n = 34).
Plugging 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.