Question 63271
Given the 6th term is - 17 and the sum upto 6 terms is -12

Let the first term be a1 and the common difference be d
Then 6th term = a1 + (6-1) * d
              = a1 + 5d

Thus a1 + 5d = - 17 -------------------(1)

Sum upto 6 terms = (6/2)*(a1+a6)
                 = 3*(a1 + -17)
                 = 3(a1 - 17)

==> 3(a1-17) = - 12
==> 3a1 - 51 = -12
==> 3a1 - 51 + 51 = - 12 + 51
==> 3a1 = 39
==> 3a1/3 = 39/3
==> a1 = 13
Plugging in a1 = 13 in (1) we get,
13 + 5d = -17
==> 13 + 5d - 13 = - 17 - 13
==> 5d = - 30
==> 5d/5 = -30/5
==> d = -6

Thus a1 = 13 and d = -6


Good Luck!!!