In a Geometric Sequence each term is found by multiplying the previous term by a common ratio except the first term and the general rule is ar^(n-1) whereas a is the first term, r is the common ratio and (n-1) is term number minus 1
an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.
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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.
Geometric sequences appear in various real-life scenarios, such as in finance through compound interest, where the amount of money grows exponentially over time. They are also found in population growth models, where populations increase by a constant percentage each period. Additionally, geometric sequences are used in technology, such as in the design of computer algorithms that reduce processing time exponentially. These applications demonstrate how geometric sequences help describe and predict growth patterns in diverse fields.
A Postulate,
how are arithmetic and geometric sequences similar
Exponentail functions
There can be no solution to geometric sequences and series: only to specific questions about them.
an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.
Follow this method:
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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.
yes a geometic sequence can be multiplication or division
An arithmetic-geometric mean is a mean of two numbers which is the common limit of a pair of sequences, whose terms are defined by taking the arithmetic and geometric means of the previous pair of terms.
There is no single rule. Furthermore, some rules can be extremely complicated.
Some of them are demographics, to forecast population growth; physicists and engineers, to work with mathematical functions that include geometric sequences; mathematicians; teachers of mathematics, science, and engineering; and farmers and ranchers, to predict crop growth and corresponding revenue growth.
A Postulate,