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38. The ratio between the sum of n terms of two airthmetic progressions is (7n+ 1):(4n+2Find the ratio of their 11th terms |
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Answer» Given ratio of sum of n terms of two AP’s = (7n+1):(4n+27)We can consider the 11th term as the m th term.Let’s consider the ratio these two AP’s m th terms as am: a’m→(2)Recall 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 [14m – 6] : [8m + 23].now substitute the value of m as 11so the answer becomes[ 14*11 - 6] : [8*11 + 23]= [ 148] : [111]= 4/3 = 4:3 |
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