Question

If 4 th term of an



a.P is 0. Then prove that 25 th term of the



a.P is three times its 11 th term.

Answer 1

a4=0

now,

a25=3(a11)

a+24d=(a+10d)3

a+24d=3 a + 30d

3a-a 30d-24d=0

2a+6d=0

a+3d=0

a4=0

Have a good day

Answer 2

Answer:Hey, brother here is your answer. It is 100% correct.

Step-by-step explanation:

1. Given, 4th term is 0.

So, by using the A.P. formula,

a+(n-1)d we get

a+(4-1)d=0

a+3d=0 or

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

So the 25th term will be given by,

a+(25-1)d ==> a+24d -----(2)

Using the value of a from (1) in (2) we get,

-3d+24d= 21d

Now again the 11th term will be given by

a+(11-1)d ==> a+10d -----(3)

Using the value of a from (1) in (3) we get,

-3d+10d= 7d.

Now if we compare the value of the 25th term with 11th term, we find that 25th term is 3 times the 11th term.

Because 7d × 3 = 21d

And we know the 25th term is also 21d.

H.T.P.

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