Question

the fourth term of an ap is zero.prove that 25th of the a.p is 3 times the 11th term

Answer 1

4th term of an ap = 0
a + 3d =0 ..........(1)

we want to prove that
a + 24d = 3 (a + 10d) .....(2)

from the equation (1) ...a = -3d
put the value of a in LHS of equation (2)
-3d + 24d = 21d ........(3)
and now put in RHS
3(-3d + 10d) = 3(7d) = 21d ......(4)

from equation (3) and (4)
a+ 24d = 3(a + 10d)

Answer 2

Given a4 = 0

 That is (a + 3d) = 0 

⇒ a = - 3d → (1) 

nth term of AP is given by

an = a + (n – 1)d a11

 = a + 10d

= – 3d + 10d

= 7d  [From (1)] 

a25 = a+ 24d

= – 3d + 24d

= 21d  [From (1)]    

    = 3 x 7d


 Hence a25 = 3 x a11