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Paragraph: Let P be the sum of first n positive terms of an increasing arithmetic progression A . Let Q be the sum of first n positive terms of another increasing arithmetic progression B . Let P: Q=(5 n+4):(9 n+6) Question: What is the ratio of their 10th terms?

Options

  1. A11 29
  2. B22 49
  3. C33 59
  4. D44 69

Correct answer

C. 33 59

Step-by-step solution

aligned & S_n S_n^ = 5 n+4 9 n+6 & 2 a+(n-1) d 2 a^ +(n-1) d^ = 5 n+4 9 n+6 aligned Put n=19 aligned & 2 a+18 d 2 a^ +18 d^ = 95+4 171+6 & a+9 d a^ +9 d^ = 99 177 a₁₀ a₁₀ ^1 = 33 59 aligned

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