Question

The 4th term of an A.P zero prove that the 25th term of the A.P is three times its 11 term
Solve fast plzzz
Give correct answer.
I mark as brainleast

Answer 1

a+3d=0
a=-3d
Term 25=a+24d = 24d - 3d =21d
Term 11 = a+10d = 10d - 3d = 7d
Therefore
3(Term 11) = Term 25

Answer 2

Given,
A4=0
To prove,
A25=(A11)*3
ATQ,
A25=a+24d. ....(i)
And,
A11=a+10d. ....(ii)
Now,
A4=a+3d
0=a+3d
a=-3d. ......(iii)
Now,
a+24d=(a+10d)*3. [Given]
-3d+24d=(-3d+10d)*3. [From (iii)]
21d=7d*3
21d=21d
21=21. [Cancelling d from both sides]
Proved.