we know that
the formula for the arithmetic sequence is
an = a1 + (n - 1)*d
where
a1 is the first term
n is the numbers of terms
for n=3 a3=-8
-8=a1+(3-1)*d-----> -8=a1+2*d-----> equation 1
for n=7 a7=32
-32=a1+(7-1)*d----> -32=a1+6*d----> equation 2
multiply equation 2 by -1-----> 32=-a1-6*d------> equation 3
add equation 1 and equation 3
-8=a1+2*d
32=-a1-6*d
----------------
24=-4*d------> d=-6
-8=a1+2*(-6) (substitute the value of d in equation 1)
-8=a1-12-----> a1=-8+12-----> a1=4
the answer is
a1=4
d=-6
