What is the difference between geometric patterns (with numbers) and arithmetic patterns?
Can you go more in depth?
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Geometric patterns and arithmetic patterns are two different types of mathematical sequences. Geometric patterns involve multiplying or dividing a number by a constant ratio, while arithmetic patterns involve adding or subtracting a constant value.
To understand the difference between the two, let's start with geometric patterns. In a geometric pattern, the sequence is formed by multiplying or dividing a constant number, known as the common ratio, to each term in the sequence. For example, consider the sequence: 2, 4, 8, 16, 32, ... In this sequence, each term is obtained by multiplying the previous term by 2. So, to find the next term, simply multiply the previous term by 2 again.
On the other hand, arithmetic patterns involve adding or subtracting a constant value from each term in the sequence. For example, consider the sequence: 3, 7, 11, 15, 19, ... In this sequence, each term is obtained by adding 4 to the previous term. So, to find the next term, simply add 4 to the previous term again.
To summarize, geometric patterns involve a constant ratio between terms, obtained through multiplication or division, while arithmetic patterns involve a constant difference between terms, obtained through addition or subtraction.