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Yes, all geometric sequences are a specific type of exponential sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio, which can be expressed in the form ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term and ( r ) is the common ratio. This structure aligns with the definition of exponential functions, where the variable is in the exponent. However, not all exponential sequences are geometric, as they can have varying bases or growth rates.
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What is the diffeence between the term to term rule and the common difference in maths?
The common difference does not tell you the location of the sequence. For example, 3, 6, 9, 12, ... and 1, 4, 7, 10, .., or 1002, 1005, 1008, 1011, ... all have a common difference of 3 but it should be clear that the three sequences are different. A common difference is applicable to arithmetic sequences, not others such as geometric or exponential sequences.
What is the difference of exponential functions and geometric series?
chicken
What are all the nth term formulas?
Nth term formulas are mathematical expressions used to find the position or value of a term in a sequence. The most common types include arithmetic sequences, where the nth term is given by ( a_n = a_1 + (n-1)d ) (with ( d ) as the common difference), and geometric sequences, represented by ( a_n = a_1 \times r^{(n-1)} ) (with ( r ) as the common ratio). For other types of sequences, such as quadratic or exponential, the nth term can be derived using specific polynomial or exponential functions. Each formula is tailored to the pattern of the sequence in question.
Do geometric sequences have a domain that includes all integers?
No, geometric sequences do not have a domain that includes all integers. The domain of a geometric sequence is typically defined for non-negative integers (whole numbers), as it is based on the term index, which starts from zero or one. While you can define a geometric sequence for negative indices by extending it, this is not standard. Thus, the standard domain is usually limited to non-negative integers.
Why belong exponential family for poisson distribution or geometric distribution?
Why belong exponential family for poisson distribution
How are arithemetic and geometric sequences similar?
how are arithmetic and geometric sequences similar
Arithmetic sequences are to linear functions as geometric sequences are to what?
Exponentail functions
What is the diffeence between the term to term rule and the common difference in maths?
The common difference does not tell you the location of the sequence. For example, 3, 6, 9, 12, ... and 1, 4, 7, 10, .., or 1002, 1005, 1008, 1011, ... all have a common difference of 3 but it should be clear that the three sequences are different. A common difference is applicable to arithmetic sequences, not others such as geometric or exponential sequences.
What is the difference of exponential functions and geometric series?
chicken
What are all the nth term formulas?
Nth term formulas are mathematical expressions used to find the position or value of a term in a sequence. The most common types include arithmetic sequences, where the nth term is given by ( a_n = a_1 + (n-1)d ) (with ( d ) as the common difference), and geometric sequences, represented by ( a_n = a_1 \times r^{(n-1)} ) (with ( r ) as the common ratio). For other types of sequences, such as quadratic or exponential, the nth term can be derived using specific polynomial or exponential functions. Each formula is tailored to the pattern of the sequence in question.
Why belong exponential family for poisson distribution or geometric distribution?
Why belong exponential family for poisson distribution
How do you solve geometric sequence and series?
There can be no solution to geometric sequences and series: only to specific questions about them.
How do arithmetic and geometric sequences compare to continuous functions?
an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.
How do you work out fraction sequences?
The answer depends on the nature of the sequence: there is no single method which will work for sequences which are arithmetic , geometric, exponential, or recursively defined.
How do you solve this word problem about geometric sequences?
Follow this method:
What is the formula for non arithmetic and geometric sequences?
because starwars is awesome
What are some examples of geometric?
There aren't any. Geometric is an adjective and you need a noun to go with it before it is possible to consider answering the question. There are geometric sequences, geometric means, geometric theories, geometric shapes. I cannot guess what your question is about.
