Q. 35.0( 1 Vote )


In a certain A.P

Answer :


Given: T 24 = 2T 10

To prove: T 72 = 2T 34

We know that,

T n = a + (n – 1)d

Therefore, T 24 = a + 23d and T 10 = a + 9d
T 72 = a + 71d
T 34 = a + 33d

Now,

T 24 = 2T 10
a + 23d = 2(a + 9d)
a + 23d = 2a + 18d

2a – a + 18d – 23d = 0
a – 5d = 0
a = 5d                                          (1)

Now let us assume, T 72 = 2T 34
a + 71d = 2(a + 33d)
a + 71d = 2a + 66d
a – 5d = 0
a = 5d                                          (2)
(2) = (1) our assumption is true
Hence proved.

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