SOLUTION: I am having trouble on this homework problem. Any help would be appreciated. Thank you. If a6=-17 and S6=-12 find a1 and d

Question 63271This question is from textbook
: I am having trouble on this homework problem. Any help would be appreciated. Thank you.
If a6=-17 and S6=-12 find a1 and d This question is from textbook

Answer by uma(370) (Show Source): You can put this solution on YOUR website!
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!!!

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