**TOUGH QUESTION** For any n = 1, the sum Sn of the first n terms in a certain arithmetic sequence is given by Sn=3n^2-n. Find an explicit formula for the general term Ar.

Question

**TOUGH QUESTION**
For any n >= 1, the sum Sn of the first n terms in a certain arithmetic sequence <Ar> is given by Sn=3n^2-n. Find an explicit formula for the general term Ar.

anonymous · Answer

Oh, I'm getting $6n-4$

anonymous · Answer

Haha, gotta love that constant term...

hartnn · Answer

$S_n=n/2(2a+(n-1)d)=n^2(d/2)+n(a-d/2)=3n^2-n$
so comparing the co-efficients,we get
d=3*2=6
a=2
so 
$T_n=a+(n-1)d=2+6n-6=6n-4$

hartnn · Answer

yup,its 6n-4

hartnn · Answer

u got that @artofspeed ?

anonymous · Answer

Here's how I did it:
$$
\sum_{i=1}^{n}ai+b=3n^2-n\implies\
\sum_{i=1}^{n} ai+\sum_{i=1}^{n}b=\frac{an(n+1)}2+bn=3n^2-n\implies\
an^2+an+2bn=6n^2-2n\implies a=6, b=-4
$$Therefore:
$$
A_n=an+b=6n-4
$$