MathematicsIf the ratio of the 11 th   term of an A.P. to its 18 th   term is 2:3  , then what is the ratio of the sum of the first five terms to the sum of its first 10 terms?

If the ratio of the 11 th   term of an A.P. to its 18 th   term is 2:3  , then what is the ratio of the sum of the first five terms to the sum of its first 10 terms?


  1. A
    17:5
  2. B
    5:17
  3. C
    17:6
  4. D
    6:17 

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    Solution:

    Given that,
    Ratio of the 11 th   term of an A.P. to its 18 th   term is 2:3  .
    We know that,
    a n =a+(n1)d  
    Then,
    a 11 a 18 = 2 3 a+10d a+17d = 2 3 3(a+10d)=2(a+17d) 3a+30d=2a+34d 3a2a=34d30d a=4d  
    The sum of terms is given by,
    S n = n 2 2a+ n1 d   Then,
    Substituting the value of ‘a’ in the formula;
    S 5 S 10 = 5 2 2a+4d 10 2 2a+9d 8d+4d 2 8d+9d 12d 34d 6 17  
    Therefore, the required ratio is 6:17.
    Hence, option 4 is correct.
     
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