SOLUTION: Please help. How do I solve this? The sum of the first n terms is Sn= n/2 (3n-17). What is the nth formula? Thank you!

Question 764514: Please help. How do I solve this?
The sum of the first n terms is Sn= n/2 (3n-17). What is the nth formula?
Thank you!
Answer by ssasr(5) (Show Source): You can put this solution on YOUR website!
The sum of n number of terms=Sn=n/2(2a+(n-1)d)
The n th term=a+(n-1)d
Given that
Sn=n/2(3n-17)
Take n=1
S1=1/2[3(1)-17]
=1/2(-14)
=-7
S1=a1
Therefore a1=-7
Now
S2=2/2[3(2)-17]
=1(-11)
S2=-11
S2=a1+a2
-11=-7+a2
-11+7=a2
a2=-4
Also
a2=a+(n-1)d
Therefore,
-7+(2-1)d=-4
-7+d=-4
d=-4+7
d=3
Now
an=a+(n-1)d
substituting values of a, d in an
an=-7+(n-1)3
=-7+3n-3
=3n-10//answer

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