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The common ratio of the geometric sequence -14,-84,-504

User Ian Oswald
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A common ratio is basically a ratio of next sequence and the sequence you want

To find a common ratio of geometric sequence, we usually define 'r' as common ratio.


\displaystyle \large \tt{r = (next \: \: sequence)/(the \: \: sequence \: \: you \: \: want) }

For example, I want to focus on -14 and the next sequence would be -84.

Hence,


\displaystyle \large{r = ( - 84)/( - 14) }

Thus, r is 6 because both numerator and denominator are negative. negative divides negative = positive.

Or you want to choose -84, then the next sequence would be -504.


\displaystyle \large{r = ( - 504)/( - 84) }

Then r would still be 6. Since both ways have r as 6 and this proves that the sequence is geometric.

Hence, the common ratio is 6.

User Asif Jalil
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