Determine the 34th term of the arithmetic sequence 97, 91, 85……
We can determine the general form of the arithmetic sequence using the formula:
a_n = a_1 + (n-1)d
where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence
n is the term number
d is the common difference between terms
In this case:
a_1 = 97
d = -6 (difference between 97 and 91)
Now we can find the 34th term:
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 is -101.