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.
a3 = 20.5 and a8 = 13
an = a1 + (n-1)d
20.5 = a1 + (3-1)d
an = a1 + (n-1)d
13 = a1 + (8-1)d
a1 = 23.5
d = -1.5
The 11th term is calculated as follows:
a11 = a1 + (n-1)d
a11= 23.5 + (11-1)(-1.5)
a11 = 8.5