darwishafizul2000 darwishafizul2000
  • 10-07-2021
  • Mathematics
contestada

Show that 4^(x+2)+4^(x+1)+4^x is divisible by 7 for all positive integers of x.​

Respuesta :

cwrw238 cwrw238
  • 10-07-2021

Answer:

Below.

Step-by-step explanation:

4^(x+2)+4^(x+1)+4^x

= 4^x*4^2 + 4^x*4 + 4^4

= 4^x(16 + 4 + 1)

= 21*4^x.

As 21 is divisible by 7, 21*4^x is also divisible by 7  for all positive integers of x.

Thus the original expression must be also divisible by 7  for all positive integers of x.

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