3, -2, a, b, -17 are terms of an A.P find a and b

3, -2, a, b, -17  are terms of an
A.P

Let us calculate the common difference
(r).

r= -2 - 3 = -5

==>
r= -5 

Now we know that:

a3 =a
= a1 + 2*r 

          = 3 +
2r

          =  3 +
2*-5

           = 3 - 10 =
-7

==> a=
-7

also:

a4 = b
= a1+ 3*r

             = 3+
3*-5

              = 3 -15 =
-12

==> b =
-12

Then
,

3, -2, -7, -12, -17    is an A.P with r =
-5