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Math Help - Geometric Sequences please help

  1. #1
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    Geometric Sequences please help

    In a question:
    Find the general term of Un which has U3 = 16 and U8=512

    --> I got the answer of Un=4*2^n-1
    which is correct,
    however,
    the answer was this:
    Un=4*2^n-1(=2^n+1)

    What does (=2^n+1) mean and where did they get it from?

    Thank you
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  2. #2
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    Quote Originally Posted by juliak View Post
    In a question:
    Find the general term of Un which has U3 = 16 and U8=512

    --> I got the answer of Un=4*2^n-1
    which is correct,
    however,
    the answer was this:
    Un=4*2^n-1(=2^n+1)

    What does (=2^n+1) mean and where did they get it from?

    Thank you
    4 \times 2^{n-1} = 2^2 \times 2^{n-1}. Do I need to spell it out from here ....?
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  3. #3
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    Hello, juliak!

    Your work is correct . . . but it can be simplified.


    Find the general term of U_n where: U_3 = 16\text{ and }U_8=512

    I got the answer of: . U_n\:=\:4\cdot2^{n-1}

    however, the answer was this: . U_n \:=\:2^{n+1}

    We have: . U_n \:=\:4\cdot2^{n-1} \;=\;2^2\cdot2^{n-1} \;=\;2^{n+1}

    Got it?

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