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Q.

If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18, … are the same, the value of n is[[1]].


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Detailed Solution

If the nth terms of the two APs: 9, 7, 5, ... and 24, 21, 18, … are the same, the value of n is 16.
The given series are 9, 7, 5, ... and 24, 21, 18, … .
From the first series,
a=9  ,
d =7−9 d =−2  
For  a n  , let’s put the values of a and d,
  a n =a+(n−1)d =9+(n−1)(−2) =9−2n+2 =11−2n  
From the second series,
a ′ −24  ,
d=21−24 d=−3  
For a n  , let’s put the values of a and d,
a n =24+ n−1 −3 =24−3 n−1 =24−3n+3 =27−3n  
Now, let’s equate both the last terms,   a n = a n 27−3n=11−2n −3n+2n=11−27 −n=−16  
n=16  
For the value of a 16   for the first AP.  a n =a+ n−1 d  
a 16 =9+ 16−1 −2 =9−15 2 =9−30 =−21  
For the value of a 16   for the second A.P.
a 16 =24+ 16−1 −3 =24−15 3 =24−45 =−21  
Thus, the correct answer is 16.
 
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