that br ay19 If the ratio of the sum of first n terms of two A.P's is

1.	that br ay19 If the ratio of the sum of first n terms of two A.P's is (7n+ 1): (an + 27), find the rati.oftheir mth terms
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 m th terms as am: a’m→(1)Recall the nth term of AP formula, an= a + (n – 1)d Hence equation (1) becomes,am: a’m= a + (m – 1)d : a’ + (m – 1)d’ On multiplying by 2, we getam: 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].

that br ay19 If the ratio of the sum of first n terms of two A.P's is (7n+ 1): (an + 27), find the rati.oftheir mth terms

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 m th terms as am: a’m→(1)Recall the nth term of AP formula, an= a + (n – 1)d

Hence equation (1) becomes,am: a’m= a + (m – 1)d : a’ + (m – 1)d’

On multiplying by 2, we getam: 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].