Question

find the middle term of an ap 20,16 to -176

Answer 1

Taking 20 as first term .

Common difference =16-20=-4

-176 = 20+(n-1)-4

-196=-4n+4

-200 = -4n

n =50


-176 is 50 th term .

Hence middle terms are 25,26 th terms.

25 th term = 20+24(-4)=20-96=-76
26th term =20+(25)(-4)=-80

Answer 2

Given AP is 20,16,12.............[-176]

 Here a = 20, d = 16 – 20 = – 4

 tn = –176 nth term of an AP is

tn = a + (n – 1)d

 ⇒–176 = 20 + (n – 1)(– 4) 

⇒ –176 = 20 – 4n + 4

 ⇒ –176 = 24 – 4n

 ⇒ –176 – 24 = –4n 

⇒ –200 = – 4n 

∴ n = 50

 The middle terms are 25th and 26th terms .

 t25 = 20 + (25 – 1)(– 4)    

  = 20 – 96 = –76
 t26 = 20 + (26 – 1)(– 4)      = 20 – 100 = –80

answer is -80