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Q.28) If the ratio of the sum of the first n terms of two A.Ps is (7n + 1):(4n+27),then find the ratio of their 9th 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 9th 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)d Hence 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 9so the answer becomes120/95. |
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