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C.B.S.E. 20145. If the ratio of the first n term of two A.P's is (7n + 1): (4n + 27), find the ratio of their mth ter |
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Answer» Given ratio of sum of n terms of two AP’s Sn:S'n = (7n+1):(4n+27)..... (1) Let’s consider the ratio these two AP’s mth terms as am: a’m. We know the nth term of AP an= a + (n – 1)dHence, 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 not able to understand |
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