find the ratio of their 11th terms, Mathematics

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The ratio of the sum of first n terms of two AP's is 7n+1:4n+27. Find the ratio of their 11th terms .

Ans: Let a₁, a₂... and d₁, d₂ be the I terms are Cd's of two AP's.

Sn of one AP = 7n+1/4n+27

Sn of II AP

m/2[2a₁ +(n-1)d₁]/ m/2 [2a₂ +(n-1)d₂] = 7n+1/4n+27

ð 2a₁ +(n-1)d₁/ 2a₂ +(n-1)d₂ = 7n+1/4n +27

ð We have sub n = 21

ð 2a₁ +20d₁/2a₂ +20d₂ = 7 x21 + 1/4(21)+27

ð A₁ +10d₁/a₂ +10d₂ = 148 /111

ð = 4/3

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