JEE Mathematics/ Lakshmikanta Satapathy/ Sequences and Series QA part 2/ JEE Question on Arithmetic Mean and Geometric Mean solved with the related concepts

1. Physics Helpline
L K Satapathy
Sequences & Series 2

2. Physics Helpline
L K Satapathy
Given that m is the A.M. of l and n
Sequence and Series 2
Question : If m is the A.M. of two distinct real numbers l and n ( l , n > 1 ) and
G1 , G2 and G3 are three geometric means between l and n , then
is equal to
4 4 4
1 2 32G G G 
2 2 2 2 2 2
( ) 4 ( ) 4 ( ) 4 ( ) 4a l mn b lm n c lmn d l m n
2 . . . (1)m l n  
4 4
. . . (2)nn l r r
l
   
Answer :
G1 , G2 and G3 are three geometric means between l and n
 l , G1 , G2 , G3 and n are in GP . Let the common ratio = r

3. Physics Helpline
L K Satapathy
Sequence and Series 2
Correct option = (b)
4 4 4 8
(1 2 )l r r r  
2 2
( ) (2 )nl l n nl m  
4 4 4 4 4 8 4 4 12
1 2 3, ,G l r G l r G l r   
2 3
1 2 3, ,G l r G l r G l r   
4 4 4 4 4 4 8 4 12
1 2 32 2G G G l r l r l r     
2
4
2
1 2n n nl
l l l
 
   
 
4 nr
l
 
  
2 2
3
2
2l nl nnl
l
    
 
4 4 4 2
1 2 32 4 [ ]G G G lm nsn A   
 2m l n 

4. Physics Helpline
L K Satapathy
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