Question

Find the general term of A.P if $S_n=3n^2+5n$. Also find $m$ if $T_m=68$

Answer 1

Sn $=\frac{n}{2}(a_1+(n-1\left)d\right)$

$=\frac{n}{2}\left(\right(a_1-d)+nd)$

$=n^2\left(\frac{d}{2}\right)+{\left(\frac{a_1-d}{2}\right)}^n$

$\therefore$ on comparing

$3=\frac{d}{2}\Rightarrow d=6$ and

$\frac{a_1-d}{2}=5\Rightarrow a_1=16$

$\therefore Tm=16+(n-1)6$

Now $T_m=68=16(m-1)6$

$72=6(m-1)$

$12=6(m-1)$

$m=13$ Answer