The ratio od sum of n …
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Ram Kushwah 6 years, 10 months ago
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)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 {tex}\frac{14m-6}{8m+23}{/tex}
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