The phrase "geometric sequence" is correct and usable in written English.
It can be used in mathematical contexts to describe a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.
Example: "The first three terms of the geometric sequence with a common ratio of 2 are 2, 4, and 8."
Alternatives: "geometric progression" or "geometric series."
The resulting geometric sequence therefore yielded a dense set of values, suitable for constructing a table.
Note that a geometric sequence can be written in terms of its common ratio; for the example geometric sequence given above: …10−3, 10−2, 10−1, 100, 101, 102, 103….
In a geometric sequence each term forms a constant ratio with its successor; for example, …1/1,000, 1/100, 1/10, 1, 10, 100, 1,000… has a common ratio of 10.
Multiplying two numbers in the geometric sequence, say 1/10 and 100, is equal to adding the corresponding exponents of the common ratio, −1 and 2, to obtain 101 = 10.
By correlating the geometric sequence of numbers a, a2, a3,…(a is called the base) and the arithmetic sequence 1, 2, 3,…and interpolating to fractional values, it is possible to reduce the problem of multiplication and division to one of addition and subtraction.
An additional substantial reduction in computing time is obtained by subsampling the analytical function at a few selected times according to a geometric sequence and then using a good quality interpolant such as the cubic spline.
The invention of logarithms was foreshadowed by the comparison of arithmetic and geometric sequences.
He doesn't make use of any of his familiar geometric sequences, and — unlike in his remarkable 1942 film "For Me and My Gal" — he doesn't keep the sexual and musical energy ratcheted tight in rhythmic choreography.
For this purpose, he generalized the traditional Chinese methods of division of the circle, using continued proportions (geometric sequences such as ax, ax2, ax3…) and an algebraic language based on analogy with arithmetic operations.
The first and the second solutions are respectively given by the arithmetic and the geometric sequences.
Again, the risk-adjusted PV can be rewritten using the law of geometric sequences (ESM of Appendix C.3).
