Question

Find the middle term of the A.P. 10,7,4,......,(-6,2).

Answer 1

SOLUTION

We have,

We have,First term a= 10

We have,First term a= 10common difference= d= -3

If A.P. contains n terms then

=) an= -62

=) a+(n-1)d= -62

=) 10+ (n-1)(-3)= -62

=) 13-3n= -62

=) 3n= 75

=) n= 75/3

=) n= 25, which is odd number.

Therefore,

middle term

$= > \frac{(n + 1)th}{2} term$

=) 25+1/2 = 26/2 = 13th term

=) a13= a+(13-1)d

=) a+ 12d

=) 10+12(-3)

=) 10-36

=) -26

hope it helps ☺️⬆️

Answer 2

SOLUTION

We have,

We have,First term a= 10

We have,First term a= 10common difference= d= -3

If A.P. contains n terms then

=) an= -62

=) a+(n-1)d= -62

=) 10+ (n-1)(-3)= -62

=) 13-3n= -62

=) 3n= 75

=) n= 75/3

=) n= 25, which is odd number.

Therefore,

middle term

= > $\frac{(n + 1)th}{2}$term=>

=) 25+1/2 = 26/2 = 13th term

=) a13= a+(13-1)d

=) a+ 12d

=) 10+12(-3)

=) 10-36

=) -26