Answer :

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


Sn = × (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 mth terms as:


Tm : T’m


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


Tm = a + (m – 1)d


T’m = a’ + (m – 1)d’


Hence the ratio of these two AP’s mth 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 7th terms of both Aps


So we have, =


=


=


the ratio of mth terms of the given 2 Aps is, 16m – 7 : 14m – 4


the ratio of 7th terms of the given 2 Aps is, 105 : 94


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