the ratio of the sum of first n terms of two

Question

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