Determine whether the sequence 36,27,18,9,... is geometric and if it is, what is the common ratio

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Tori Knight · Accepted Answer

In a geometric sequence, ratio of a term and its immediately preceding term is always constant.In other words, to determine whether a sequence             a      1        ,          a      2        ,          a      3        ,          a      4        ,          a      5        ,    ...    ...    ...    ...    .   is a geometric sequence or not, one should check the ratios                     a        2                    a        1              ,                  a        3                    a        2              ,                  a        4                    a        3              ,                  a        5                    a        4             and if they are all equal i.e.                    a        2                    a        1              =                  a        3                    a        2              =                  a        4                    a        3              =                  a        5                    a        4            , then the sequence             a      1        ,          a      2        ,          a      3        ,          a      4        ,          a      5        ,    ...    ...    ...    ...    .   is a geometric sequence.Here in the series 36,27,18,9,.......the ratios are             27      36        ,          18      27        ,          9      18      , which can be simplified to             3      4        ,          2      3        ,          1      2       and as ratios are different, the series 36,27,18,9,....... is not a Geometric sequence.Here, in fact we have 27−36=18−27=9−18=−9 and what we have is that they have common difference and hence the series 36,27,18,9,....... is an arithmetic sequence.

Determine whether the sequence 36,27,18,9,... is geometric and if it is, what is the common ratio

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