Question

the 4th term of an A.P is zero prove that 25th term of the A.P is three times its 11th term

Answer 1

Hi ,

Let a and d are the first term and

common difference of an A.P

It's given that ,

a4 = 0

a + 3d = 0

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

a25 = a + 24d

= - 3d + 24d [ from ( 1 ) ]

= 21d ---( 2 )

a11 = a + 10d

= - 3d + 10d

= 7d ------( 3 )

From ( 2 ) and ( 3 ) , we observe that

a25 = 3 × a11

21d = 3 × 7d

I hope this helps you.

: )

Answer 2

a + 3d = 0
a = -3d

To prove: a + 24d = 3(a + 10d)

LHS

a + 24d
= -3d + 24d (a = -3d)
= 21d

RHS

3(a + 10d)
= 3(-3d + 10d) (a = -3d)
= 3(7d)
= 21d

Since, LHS = RHS
Hence, proved

Hope this helps!!!
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