Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence. 1, 3, 9, 27, 81,…

Question

Determine whether the sequence below is a geometric sequence and, if so, find a formula that describes the sequence. 1, 3, 9, 27, 81,…

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    0
    2021-09-04T13:26:46+00:00

    This is a geometric sequence.

    from 1-3 one is multiplied by three

    from 3-9 three is multiplied by three

    from 9-27 nine is multiplied by three

    and from 27-81 27 is multiplied by three

    Hope this helped!!

    |Sophia M|

    0
    2021-09-04T13:26:48+00:00

    a geometric sequence is a bunch of numbers where you can get from a number to the next number by multiplying the previous number by a certain number

    might be confusing so here’s an example

    1,2,4,8,16

    each term is multiplied by 2 to get next term, that number that each term is multiplied by is called the common ratio

    formula for geometric sequence is

    a_n=a_1(r)^{n-1}

    where a_n is nth term

    a_1 is first term

    r is teh common ratio

    n=which term

    in our example

    1,3, 9, 27, 81

    each term is being multiplied by 3 so it is a geometric sequence and thus r=3

    also first term is 1 so a_1=1

    so the formula is a_n=1(3)^{n-1} or in function notation f(n)=1(3)^{n-1}

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