Question Video: Finding the Common Ratio of a Given Geometric Sequence | Nagwa Question Video: Finding the Common Ratio of a Given Geometric Sequence | Nagwa

Question Video: Finding the Common Ratio of a Given Geometric Sequence Mathematics • Second Year of Secondary School

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The table shows the number of bacteria in a laboratory experiment across four consecutive days. The number of bacteria can be described by a geometric sequence. Find the common ratio of this sequence.

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Video Transcript

The table shows the number of bacteria in a laboratory experiment across four consecutive days. The number of bacteria can be described by a geometric sequence. Find the common ratio of this sequence.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant. The formula for the 𝑛th term of a geometric sequence is π‘Ž sub 𝑛 is equal to π‘Ž times π‘Ÿ to the 𝑛 minus one power, where π‘Ž is equal to the first term. If the bacterial growth can be represented as a geometric sequence, it means that there is some constant π‘Ÿ we can multiply the day one’s bacteria by to get day two’s bacteria.

This means we can say 643 times π‘Ÿ will be equal to 2,572. If we divide both sides of this equation by 643, we get that π‘Ÿ equals four. We’re then saying that the common ratio would be four. We can check that this is true for the other days. If π‘Ÿ is the common ratio, then 2,572 times four should equal 10,288, which it does, and 10,288 times four should equal 41,152, which it does. The common ratio in the geometric sequence that represents this experiment will be four.

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