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Q.

How many terms of the AP: 9,17,25, … must be taken to give a sum 636?


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a

78

b

5

c

14

d

12 

answer is D.

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Detailed Solution

Given that AP: 9,17,25, …
We know that, the sum of nth terms, S n = n 2 (2a+(n−1)d)  .
From the given AP, a = 9
And d = 8
Sum(Sn) = 636
⇒636= n 2 (2(9)+(n−1)8) ⇒636=n(9+4n−4) ⇒636=n(4n+5) ⇒4 n 2 +5n−636=0  
⇒4 n 2 +53n−48n−636=0 ⇒n(4n+53)−12(4n+53) ⇒(4n+53)(n−12)=0 ⇒n= −53 4 ,12  
The number of terms cannot be in fraction, so, n=12  is the required answer.
Hence, the number of terms in the given AP to get the sum 636 is 12.
Therefore, the correct answer is option (4).
 
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