Question

if the third term of an arithmetic sequence is 13 and the seventeenth term is -29 what is the eighth term

Answer 1

We know that
the nth term of an arithmetic sequence can be written in the following way:

an = a1+(n - 1)d

Where a1 is the first term, and d is the common difference.

for a3=13  n=3
a3=a1+(n-1)*d----> 13=a1+(3-1)*d----> 13=a1+2*d-----> equation 1

for a17=-29  n=17
a17=a1+(n-1)*d----> -29=a1+(17-1)*d----> -29=a1+16*d-----> equation 2

using a graph tool------> to resolve the equations system
see the attached figure
the solution is 
a1=19
d=-3

find a8
a1=19  d=-3   n=8
a8=19+(8-1)*(-3)----> a8=19+(-21)------> a8=-2

the answer is
a8 is -2