# The ratio of sum

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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