Question

If 5²×5⁴........5²n =(0.04)²¹
what's it's nth term​

Answer 1

$5^{2}$×$5^{4}$×......×$5^{2n}$ = (0.04)²¹

RHS = (0.04)²¹

       = (4/100)²¹

       = (1/25)²¹

       = (5⁻²)²¹

       = 5⁻⁴²

LHS = $5^{2}$×$5^{4}$×......×$5^{2n}$

       = $5^{(2+4+....+2n)}$

       = $5^{2(1+2+....+n)}$

       = $5^{2\frac{n(n+1)}{2} }$

       =  $5^{n(n+1)}$

Equating LHS and RHS, we get

$5^{-42}$ = $5^{n(n+1)}$

-42 = n(n+1)

n²+n+42 = 0

Solving the above quadratic equation, we find that it has no real roots

Hence there is no real value for n that can satisfy

$5^{2}$×$5^{4}$×......×$5^{2n}$ = (0.04)²¹

HOPE IT HELPS !!

Answer 2

Answer:

Thomas Anderson, a computer programmer, is led to fight an underground war against powerful computers who have constructed his entire reality with a system called the Matrix.

Initial release: 31 March 1999 (USA)

Directors: Lana Wachowski, Lilly Wachowski

Box office: 46.53 crores USD

Film series: The Matrix

Screenplay: Lana Wachowski

Step-by-step explanation:

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