Answer :

Let the sum of n terms of the first A.P be:

⇒ S_{n} = × (2a + (n – 1)d) …………… (1)

Let the sum of n terms of the second A.P be:

⇒ S’_{n} = × (2a’ + (n – 1)d’) …………… (2)

Now according to the question:

⇒ =

Let’s consider the ratio these two AP’s m^{th} terms as:

T_{m} : T’_{m}

Now, recall that, nth term of an AP is T_{n} = a + (n – 1)d

⇒ T_{m} = a + (m – 1)d

⇒ T’^{m} = a’ + (m – 1)d’

Hence the ratio of these two AP’s m^{th} terms become:

⇒ =

On multiplying by 2, we get,

⇒ =

⇒ =

⇒ =

⇒ =

⇒ =

⇒ =

Now from the above formula of the ratio of mth terms of 2 Aps, we can find the ratio of 7^{th} terms of both Aps

So we have, =

⇒ =

⇒ =

∴ the ratio of m^{th} terms of the given 2 Aps is, 16m – 7 : 14m – 4

∴ the ratio of 7^{th} terms of the given 2 Aps is, 105 : 94

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