The ratio of the sum of n terms of two A.P\'s is (7n+1) : (4n+27) find the ratio of their mth terms

The ratio of the sum of n terms of two A.P\'s is (7n+1) : (4n+27) find

1.	The ratio of the sum of n terms of two A.P\'s is (7n+1) : (4n+27) find the ratio of their mth terms
Answer» Sn=n/2(2A+(n-1)D)/n/2(2a+(n-1)d=7n+1/4n+272A+(n-1)D/2a+(n-1)d=7n+1/4n+27N=22A+(17-1)D/2a+(17-1)d=120/952A+16D/2a+16d=120/95A+8D/a+8d=120/95Ratio 24:19 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\xa0Recall the nth term of AP formula, an = a + (n – 1)dHenceam : 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]