# Is the sequence -2, -1, -frac{1}{2}, -frac{1}{4}, cdots geometric? If so find the common ratio. If not, explain why

Is the sequence geometric? If so find the common ratio. If not, explain why
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Step 1 To Determine: Given sequence is geometric or not. Step 2 Explanation: When given sequence is geometric, it is must have common ratio. Common ratio is a ratio just divide each number from the number preceding it in the sequence. In given sequence, ratio of is: $\frac{-1}{-2}=\frac{1}{2}$

$\frac{-\frac{1}{2}}{-1}=\frac{1}{2}$

$\frac{-\frac{1}{4}}{-\frac{1}{2}}=\frac{2}{4}=\frac{1}{2}$ We see that, all ratio are same So, common ratio : $r=\frac{1}{2}$ It means given sequence is geometric sequence