Question

Find the middle term of the A.P. $213,205,197,..........,137.$

Answer 1

$213,205,197,......137$

In the given $AP$ $a=213,d=-8$

and last term is $137$

we have, $t_n=a+(n-1)d$

$137=213+(n-1)(-8)\Rightarrow (n-1)(-8)=137-213(n-1)(-8)=-76\Rightarrow 2n-2=19\Rightarrow 2n=21\Rightarrow n=\frac{21}{2}=10$

Middle term means $5th$ term

$t_5=213+(5-1)(-8)=213-8\times 4=213-32=181$