Question

4th term of an ap is zero then prove that 25th term is 3 times the 11 tyh term

Answer 1

4th term of an a.p = a^4 = 0
a+3d = 0
a= -3d

25th of an a.p = a^25 = 0
a+24d =0
-3d + 24d = 0
= 21d

3 times 11th of an a.p = 3a^11
= 3(a+10d)
= 3(-3d+10d)
= 3×7d
= 21d

hence proved

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Answer 2

Given :- a4 = 0

To prove :- a25 = 3 ( a 11 )

an = a + ( n - 1 )d


a4 = a + 3d

0 = a + 3d

a = - 3d

___________

• a 25 = a + 24d

- 3d + 24d = 21d

____________

• a11 = a + 10d

- 3d + 10d = 7d


____________

Since , a25 = 3 ( a11 )

21d = 3 ( 7d )

Hence proved !