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

The ratio od sum of n terms of two A.P.s is (7n +1):(4n+27).Find the r

1.	The ratio od sum of n terms of two A.P.s is (7n +1):(4n+27).Find the ratio of \'m\'th terms.
Answer» Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27)....(1)Let’s consider the ratio these two AP’s mth terms as am : a’m →(2)The nth term of AP formula, an = a + (n – 1)dHence equation (2) 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 {tex}\\frac{14m-6}{8m+23}{/tex}