Question

if the ratio of the sum of first n terms of two ap is 7 and + 14 and + 27 find the ratio of their 9th term​

Answer 1

Step-by-step explanation:

this.

is.

the.

answer.

Answer 2

Answer:

24 : 19 is the answer

Step-by-step explanation:

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

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

Let’s consider the ratio these two AP’s nth terms as an : a’n →(2)

Recall the nth term of AP formula, an = a + (n – 1)d

Hence equation (2) becomes,

an : a’n = a + (n – 1)d : a’ + (n – 1)d’

On multiplying by 2, we get

an : a’n = [2a + 2(n – 1)d] : [2a’ + 2(n – 1)d’]

= [2a + {(2n – 1) – 1}d] : [2a’ + {(2n – 1) – 1}d’]

= S2n – 1 : S’2n – 1 

= [7(2n – 1) + 1] : [4(2n – 1) +27] [from (1)]

= [14n – 7 +1] : [8n – 4 + 27]

= [14n – 6] : [8n + 23]

Thus the ratio of nth terms of two AP’s is [14n – 6] : [8n + 23].

now substitute n as 9

therefore the answer becomes

120/95 = 24/19 = 24 : 19

hope it helps u