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Manipal MET2021MathematicsSequences and Series

The sum of the first n terms of two AP's are in the ratio (2 n+3):(3 n-1) . The ratio of the 5th terms is

Options

  1. A11: 6
  2. B21: 26
  3. C13: 16
  4. D8: 5

Correct answer

B. 21: 26

Step-by-step solution

array ll Let & S_ m₁ = n 2 [2 a₁+(n-1) d₁ ] and & S_ n₂ = n 2 [2 a₂+(n-1) d₂ ] & n 2 [2 a₁+(n-1) d₁ ] n 2 [2 a₂+(n-1) d₂ ] = 2 n+3 3 n-1 array (given) For 5th term, replace n by 2 5-1=9 aligned & 2 a₁+8 d₁ 2 a₂+8 d₂ = 18+3 27-1 & a₁+4 d₁ a₂+4 d₂ = 21 26 aligned

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