Answer
c) carter
Explanation
Remember that A geometric sequence is a sequence where each term after the first is found by multiplying the previous term by a fixed number called the ratio. So to prove if a sequence is geometric, y we just need to verify that the ratio between any tow terms of the sequence is the same.
Now, to find the ratio of a geometric sequence, we use the formula:
\(r=\frac{a_{n}}{a_{n-1}}\)
\(r\) is the ratio
\(a_{n}\) is the current term
\(a_{n-1}\) is the previous term
The formula just mean that we can find the ratio by dividing the current term and the previous term.
Let's apply this to our sequences:
Angela -6,-9,-12,-15,...
Take -9 as the current term and -6 as the previous term, so \(a_{n}=-9\) and \(a_{n-1}=-6\); now let's find the ratio.
\(r=\frac{a_{n}}{a_{n-1}}\)
\(r=\frac{-9}{-6} =\frac{3}{2}\)
Lets check if the ratio hold for the next pair -9 and -12. \(a_{n}=-12\) and \(a_{n-1}=-9\), so
\(r=\frac{-12}{-9} =\frac{4}{3}\)
The ratio is not the same, so Angela's sequence is not a geometric one.
Bradley -2,-6, -12,-24,...
For -2 and -6
\(r=\frac{a_{n}}{a_{n-1}}\)
\(r=\frac{-6}{-2} =3\)
For -6 and -12
\(r=\frac{-12}{-6} =2\)
The ratio is not the same, so Bradley's sequence is not a geometric one.
Carter -1, -3, -9, -27,...
For -1 and -3
\(r=\frac{-3}{-1} =3\)
For -3 and -9
\(r=\frac{-9}{-3} =3\)
For -9 and -27
\(r=\frac{-27}{-9} =3\)
The ratio is always the same, so Carter's sequence is a geometric one.
Dominique -1, -3,-9, -81,...
For -1 and -3
\(r=\frac{-3}{-1} =3\)
For -3 and -9
\(r=\frac{-9}{-3} =3\)
For -9 and -81
\(r=\frac{-81}{-9} =9\)
The ratio is not the same, so Dominique's sequence is not a geometric one.
