Question

Find the middle term if 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)
Tn=37..........(a)
Now, Tn =a+(n-1)d
213+(n-1)(-8)
213-8n+8
Tn=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+1/2. (for odd numbers)
middle term=23+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..

Answer 2

hope it will help you