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.
chicken
Why belong exponential family for poisson distribution
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.
an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.
how are arithmetic and geometric sequences similar
Exponentail functions
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.
chicken
There can be no solution to geometric sequences and series: only to specific questions about them.
Why belong exponential family for poisson distribution
an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.
Follow this method:
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.
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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.
Poisson distribution or geometric distribution