Find the rth term of an A.P., the sum of whose first n terms is


Find the rth term of an A.P., the sum of whose first n terms is 3n2 + 2n.                                      [NCERT EXEMPLAR]


Let $a$ and $d$ be the first term and the common difference of the given A.P., respectively As, $S_{n}=3 n^{2}+2 n$

So, $a=S_{1}=3 \times 1^{2}+2 \times 1=3+2=5$ and

$S_{2}=3 \times 2^{2}+2 \times 2=12+4=16$

$\Rightarrow a+a_{2}=16$

$\Rightarrow a+a+d=16$

$\Rightarrow 2 a+d=16$

$\Rightarrow 2 \times 5+d=16$

$\Rightarrow d=16-10$

$\Rightarrow d=6$


$a_{r}=a+(r-1) d$

$=5+(r-1) \times 6$

$=5+6 r-6$

$\therefore a_{r}=6 r-1$

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