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.

Answer Link

Otras preguntas

Rewrite the expression by factoring out the GCF 36y to the second power + 54y Thanks a billion Brainly students !!! :D
AHHH Help thank you 1-4 <_<
2x+3y=6 X+2y=5 Solve by elimination
is 14.5℅ equivalent to 14.5
All Sumerian cities built ziggurats the same size. A. True B. False
World War I and World War II were both concentrated in ____ and ____ in scope.
Why did the United States expand its role in Latin America in the early 1900s
Describe the structure of a female cone in a plant.
How does the Supremacy Clause affect US judges? A. The Supremacy Clause states that judges can amend state laws. B. The Supremacy Clause states that no judge ca
What is a sentence with the word abound