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If the ratio of sn of the first n terms of two APs (7n+1) : (4n+27) than find the ratio of the 9th term

Posted by Ayush Bandhu 6 years, 11 months ago

CBSE > Class 10 > Mathematics

3 answers

Puja Sahoo?‍♀️ 6 years, 11 months ago

24:19

Lavina Rajput ??? 6 years, 11 months ago

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 get am : 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 9 so the answer becomes 120/95 = 24/19

Anshika & Aliens???? 6 years, 11 months ago

I think 64:63

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