Question

Find the middle term of the A.P. 213,205,197,...,37.

Answer 1

Solution-
In this AP(213,205,197,....,37),
first term'a'=213
common difference'd'=205-213=(-8)
$T_n$ =37..........(a)
Now $T_n$ =a+(n-1)d
=213+(n-1)(-8)
=213-8n+8
$T_n$ =221-8n
using(a)
37=221-8n
37-221=(-8n)
(-184)=(-8n)
184/8=n
23=n
hence this AP contains 23 terms..
middle term= $(n+1)\frac{1}{2}$ (for odd numbers)
middle term= $(23+1)\frac{1}{2}$
=24/2
=12th term
so, the middle term of this AP is its 12th term..
12th term=a+(12-1)d
=213+11*(-8)
=213-88
=125
so the middle term of this AP is 12th term
and the value of 12th term is 125..