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

Question

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

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Sapo 1 week 2021-07-21T20:48:38+00:00 1 Answers 1 views 0

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    2021-07-21T20:49:58+00:00

    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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