# In an AP, the sum of n terms is a function of n, $S_{n}=3n^2+2n.$ Find the rth term.

$\begin{array}{1 1} r-6 \\ 6r-1 \\ 1- 6r \\ 6-r \end{array}$

Answer : (b) 6r-1
Explanation : $S_{n}=3n^2+2n$
$For\; n=1\qquad\;S_{1}=3+2=5$
$For\; n=2\qquad\;S_{2}=3(2)^2+2(2)=16$
$S_{1}=a=5$
$S_{2}=a+a+d=16$
$d=16-10=6$
$rth\; term=a+(r-1)d=5+(r-1)6$
$T_{r}=5+6r-6$
$=6r-1.$
answered Dec 30, 2013 by