Question

The 4th term of the ap is zero prove that the 25th tetm of the ap is three time it's 11th term

Answer 1

4th term = a+ 3d = 0
from this, we get
a = -3d

25th term = a + 24d
=> -3d + 24 d
=> 21d

3times the 11th term
=> 3[ a+10d]
=> 3(-3d + 10d)
=> 21d

LHS = RHS
Hence proved.

Answer 2

Given,

4th term of the A.P. = 0

=> a + (4 - 1)d = 0

=> a + 3d = 0

=> a = - 3d ------------------------------>(1)


Now,

25th term of the A.P. = a + (25 - 1)d
= a + 24 d
= - 3d + 24d [ From (1) ]
= 21d


3 time of 11th term of the A.P. = 3 { a + (11 - 1)d }
= 3 { ( - 3d ) + 10d} [ From (1) ]
= 3 ( - 3d + 10d )
= 3 × 7d
= 21d

°•° 25th term of the A.P. = 3 times of the 11th term of the A.P. = 21 d


Hence proved.