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  • How many terms of the Arithmetic Progression 45, 39, 33, ... must be taken so that their sum is 180 ? Explain the double answer.      

How many terms of the Arithmetic Progression 45, 39, 33, ... must be taken so that their sum is 180 ? Explain the double answer.

 

 
 
 
 
 

Answers (1)

AP = 45, 39, 33, ...

S_n = 180,    a = 45

n = ?    d = 39-45 = -6

S_n = 180 = \frac{n}{2}\left[2a + (n-1)d \right ]

\Rightarrow 180 = \frac{n}{2}\left[90 + (n-1)(-6) \right ]

\Rightarrow 360 = 90n - 6n^2 + 6n

\Rightarrow 6n^2 - 96n + 360 = 0

\Rightarrow 6[(n-6)(n-10)] = 0

\Rightarrow n = 6 , \ n = 10

 

Posted by

Safeer PP

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