Question

Find the middle term of the A.P. $213,205,\mathrm{197....37}$

Answer 1

Let $a=$ first term of A.P., $d=$common difference

$n^{th}$ term, $a_n=a+(n-1)d$;

Here $a=213$, $d=205-213=-8,a_n=37$

$a_n=a+(n-1)d$

$\Rightarrow 37=213+(n-1)(-8)$

$\Rightarrow 176=8(n-1)$

$\Rightarrow 8n=184$

$\Rightarrow n=23$

$\Rightarrow$ Middle term $=\frac{23+1}{2}={12}^{th}$ term

$\Rightarrow a_{12}=a+11d=213-88=125$.