Question

If the ratio of the sum of first n terms of two A.P.'s is (7n+1): (4n+27), find the ratio of their mth terms. ​

Answer 1

Answer:

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…..(2)

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 – 2)d] : [2a’ + (2m – 2)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].