Question

if the ratio of the sum of first n terms of two ap is (7 n+ 1):(4n + 27). Then find the ratio of their 9th terms.

Answer 1

Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27)

We can consider the 9th term as the m th term.

Let’s consider the ratio these two AP’s m th terms as am : a’m →(2)

Recall the 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] [from (1)]

= [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].

now substitute the value of m as 9

so the answer becomes

120/95

hope it helps u