In order to solve for a nth term in an arithmetic sequence, we use the formula written as:
an = a1 + (n-1)d
where an is the nth term, a1 is the first value in the sequence, n is the term position and d is the common difference.
First, we need to calculate for d from the given values above.
a9 = 64 and a12 = 88
an = a1 + (n-1)d
64= a1 + (9-1)d
an = a1 + (n-1)d
88= a1 + (12-1)d
a1 = 0
d = 8
The 6th term is calculated as follows:
a6 = 0 + (n-1)d
a6= (6-1)(8)
a6 = 40