Find the 3nd term for 7.13.19
how are arithmetic and geometric sequences similar
Exponentail functions
Arithmetic : (First term)(last term)(act of terms)/2 Geometric : (first term)(total terms)+common ratio to the power of (1+2+...+(total terms-1))
1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN < ARITHMETIC MEAN 2.
The difference between arithmetic and geometric mean you can find in the following link: "Calculation of the geometric mean of two numbers".
how are arithmetic and geometric sequences similar
Exponentail functions
an arithmetic sequeunce does not have the sum to infinty, and a geometric sequence has.
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.
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Arithmetic : (First term)(last term)(act of terms)/2 Geometric : (first term)(total terms)+common ratio to the power of (1+2+...+(total terms-1))
Arithmetic and geometric sequences are similar in that both are ordered lists of numbers defined by a specific rule. In an arithmetic sequence, each term is generated by adding a constant difference to the previous term, while in a geometric sequence, each term is produced by multiplying the previous term by a constant factor. Both sequences can be described using formulas and have applications in various mathematical contexts. Additionally, they both exhibit predictable patterns, making them useful for modeling real-world situations.
There is no simple answer. There are simple formulae for simple sequences such as arithmetic or geometric progressions; there are less simple solutions arising from Taylor or Maclaurin series. But for the majority of sequences there are no solutions.
A few examples: Counting numbers are an arithmetic sequence. Radioactive decay, (uncontrolled) bacterial growth follow geometric sequences. The Fibonacci sequence is widespread in nature.
Geometric
1.The Geometric mean is less then the arithmetic mean. GEOMETRIC MEAN < ARITHMETIC MEAN 2.
they look like arithmetic and geometric patterns in math