The ratio of the sum of n terms of two A.P's is (7n+1):(4n+27) . Find the ratio of m terms

Given that ratio of sum of n terms of two AP’s = (7n+1):(4n+27)
Let us assume the ratio of these two AP’s mth terms as am : a’m
We know that nth term of AP formula, an = a + (n – 1)d
Hence equation (2) becomes,
am : a’m = a + (m – 1)d : a’ + (m – 1)d’
On multiplying by 2, we get
am : a’m = [2a + 2(m – 1)d] : [2a’ + 2(m – 1)d’]= [2a + {(2m – 1) – 1}d] : [2a’ + {(2m – 1) – 1}d’]= S2m – 1 : S’2m – 1
= [7(2m – 1) + 1] : [4(2m – 1) +27] [14m – 7 +1] : [8m – 4 + 27]= [14m – 6] : [8m + 23]Thus the ratio of mth terms of two AP’s is [14m – 6] : [8m + 23].

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