Question 1041613
{{{a[1]=-24}}}
{{{a[n]=3}}}
{{{S[n]=1230}}}
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On the face of it, you're adding a bunch of negative numbers (if the difference between the two numbers is 9, then 3 is the only positive number) to get a large positive sum.
Something is wrong with your problem setup. 
Please check it and repost with a corrected question.