If the ratio of the sum of the first n terms of two A.Ps is (7n + 1):

1.	If the ratio of the sum of the first n terms of two A.Ps is (7n + 1): (4n+27nthen find the ratio of their 9th terms.
Answer» Answer. Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27) Let’s consider the ratio these two AP’s mth 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]. So, the ratio of 9th term=14(9)-6: 8(9)+23120:95=24:19 hit like if you find it useful

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1): (4n+27nthen find the ratio of their 9th terms.

Answer»

Answer.

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

Let’s consider the ratio these two AP’s mth 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].

So, the ratio of 9th term=14(9)-6: 8(9)+23120:95=24:19

hit like if you find it useful