Question

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

Answer 1

Answer:

1_-8-4-1

...............

Answer 2

SOLUTION

Given,

First term, a=10

common 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)

Therefore,

The Middle term

$= > \frac{(n + 1)th}{2} term \\ \\ = > \frac{25 + 1}{2} term = \frac{26}{2} \\ \\ = > 13th \: term$

Hence,

a13= a+(13-1)d

=) a+12d

=) 10+12(-3)

=) 10-36

=) -26

Hope it helps ☺️