Problem

What is the common ratio between successive terms in the sequence? $1.5,1.2,0.96,0.768, \ldots$ $-0.8$ $-0.3$ 0.3 0.8

Solution

Step 1 :The common ratio between successive terms in a geometric sequence can be found by dividing any term by the previous term. In this case, we can divide the second term by the first term, or the third term by the second term, and so on. This should give us the common ratio.

Step 2 :Let's calculate the ratio using the first two terms of the sequence: \(\frac{1.2}{1.5}\).

Step 3 :The ratio calculated is approximately 0.8. However, due to the limitations of floating point arithmetic, the result is not exactly 0.8 but very close to it. We can round the result to get a more accurate representation.

Step 4 :Final Answer: The common ratio between successive terms in the sequence is \(\boxed{0.8}\).

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Source: https://solvelyapp.com/problems/17210/

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