12) How are arithmetic and geometric sequences different?a) Arithmetic sequences have a common difference while geometric sequences have a common ratiob) Both sequences have a common ratioc) Arithmetic sequences have a common ratio while geometric sequences have a common differenced) Both sequence are defined recursively
Question
- How are arithmetic and geometric sequences different?a) Arithmetic sequences have a common difference while geometric sequences have a common ratiob) Both sequences have a common ratioc) Arithmetic sequences have a common ratio while geometric sequences have a common differenced) Both sequence are defined recursively
Solution
The correct answer is a) Arithmetic sequences have a common difference while geometric sequences have a common ratio.
Here's why:
Arithmetic sequences are sequences where each term after the first is obtained by adding a constant difference to the previous term. For example, in the sequence 2, 4, 6, 8, the common difference is 2.
On the other hand, geometric sequences are sequences where each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 3, 6, 12, 24, the common ratio is 2.
So, the main difference between arithmetic and geometric sequences lies in how the next term in the sequence is obtained - by addition in arithmetic sequences and by multiplication in geometric sequences.
Similar Questions
Explain the difference between an arithmetic sequence and a geometric sequence. Givean example of each type of sequence as part of your explanation
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8) In a geometric sequence, what remains constant?a) The product of consecutive termsb) The ratio between consecutive termsc) The difference between consecutive termsd) The sum of consecutive terms
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