Explain the difference between an arithmetic sequence and a geometric sequence. Givean example of each type of sequence as part of your explanation
Question
Explain the difference between an arithmetic sequence and a geometric sequence. Give an example of each type of sequence as part of your explanation
Solution
An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is known as the common difference. For example, the sequence 2, 4, 6, 8, 10 is an arithmetic sequence with a common difference of 2.
On the other hand, a geometric sequence is a sequence of numbers in which the ratio of any two consecutive terms is constant. This ratio is known as the common ratio. For example, the sequence 3, 6, 12, 24, 48 is a geometric sequence with a common ratio of 2.
In summary, an arithmetic sequence grows by adding a constant difference, while a geometric sequence grows by multiplying by a constant ratio.
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