Tuesday, May 3, 2016

`3, 12, 21, 30...` Determine whether the sequence is geometric. If so, find the common ratio.

You need to verify if the sequence is a geometric sequence, hence, you need to use the following property, such that:


`a_n = sqrt(a_(n-1)*a_(n+1))`


Replacing 12 for `a_n` , 3 for `a_(n-1)` and 21 for `a_(n+1)` yields:


`12 = sqrt(3*21) => 12 = sqrt(3^2*7) => 12 != 3sqrt7`


Since the given sequence is not geometric, the ratio cannot be found.

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