Question

Q. If the ratio of the sum of the first n terms of two APs is (7n+1):(4n+27) then find the ratio of their 9th term.

Answer 1

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

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

Let’s consider the ratio these two AP’s m^th terms = am : Am ------------(2)

An = a + (n – 1)d

Hence in eq--(2)

am : Am = a + (m – 1)d : A + (m – 1)D

On multiplying by 2, we get

am : Am = [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 m^th terms of two AP is:

[14m – 6] : [8m + 23].

On substituting the value of m = 9

We get,

120/95

Mark it as the brainliest plzzzzz.