if 52 x 54 x 56x --------------- 52n = ( 0.04) - 28 what is n ?

Answer:
Given

52 × 54 × 56 × ............................... ×52n    = ( 0.04 )-28

So,

5( 2 + 4 + 6 + ........... + 2n )   = 125-28

5( 2 + 4 + 6 + ........... + 2n )  = ( 25 ) 28

5( 2 + 4 + 6 + ........... + 2n )  = 556 

Here we can see that ( 2 + 4 + 6 + ........... + 2n ) is a arithmetic progression ,
We know , formula of sum of n terms of arithmetic progression is 

S = n2[ 2a+ ( n - 1 ) d ] , Where 

a1 = 2 And d = 2  And n = 2n , So

S = 2n2[ 4 + ( 2n - 1 ) 2 ]

S = n [ 4 + 4n - 2 ]

S = 4n2 + 2n
So

 5  4n2 + 2n    = 5 56

Comparing both side we get

4n2 + 2n = 56 

2n2 +  n - 28 = 0

Now we use quadratic equation to find zeros of the equation is
n-b ±b2-4ac2a
Here a = 2 , b = 1 and c  = -28 So,

-1 ±12-4×2×-282×2

-1 ±1+2244

-1 ±154

So 

n = - 4 And  72                           ( Ans )


 

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Go to textbook solutions mathematics part 1 ,arithematic sequence,page 25 and question number 3

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