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

The narrator in Poe's story told readers about events from the: A) first person point of view. B) second person point of view. C) third person point of view. D)
Choose the linking verb in the sentence: I will be a freshman in high school next year.
If the circumference of circular field is 16 π cm . The area of the field is
Tom can walk 5 blocks in 10 minutes. How many blocks can tom walk in 35 minutes
please help and if u dont know that ok but pleas don't give me the wrong answer​
HEY CAN ANYONE PLS ANSWER DIS IN UR OWN WORDS (SPANISH)
I need help on this one
An arts academy requires there to be 5 teachers for every 120 students and 3 tutors for every 24 student. How many students does the academy have per​ teacher?
Explain in a short sentence how you can tell if a reaction is a single replacement reaction.
Name three percussion instruments which were added to the Romantic orchestra