To determine the common ratio of the given sequence \( 27, 9, 3, 1, \frac{1}{3}, \frac{1}{9}, \frac{1}{27}, \ldots \), we need to examine the ratio between successive terms.
Let's calculate the ratio between the first and second terms:
\[ \frac{9}{27} = \frac{1}{3} \]
Now, check the ratio between the second and third terms:
\[ \frac{3}{9} = \frac{1}{3} \]
Continuing this way, let's verify for the third and fourth terms:
\[ \frac{1}{3} \]
This confirms that the ratio between successive terms consistently is \( \frac{1}{3} \).
Therefore, the common ratio for the sequence is:
\[ \frac{1}{3} \]
What is the common ratio between successive terms in the sequence?
27, 9, 3, 1, one-third, one-ninth, StartFraction 1 over 27 EndFraction, ...
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1 answer