If the nth term is Tn, the ratios of consecutive terms are Tn+1/Tn for n = 1, 2, 3, ... This will be a constant only for geometric sequences.
No. Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one. A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
Yes, that's what a geometric sequence is about.
You mean what IS a geometric sequence? It's when the ratio of the terms is constant, meaning: 1, 2, 4, 8, 16... The ratio of one term to the term directly following it is always 1:2, or .5. So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.
Ratio
It is a constant, other than 0 or 1.
Well, honey, neither. That sequence is a hot mess. In an arithmetic sequence, you add the same number each time, and in a geometric sequence, you multiply by the same number each time. This sequence is just doing its own thing, so it's neither arithmetic nor geometric.
A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.
No, the Fibonacci sequence is not an arithmetic because the difference between consecutive terms is not constant
If the nth term is Tn, the ratios of consecutive terms are Tn+1/Tn for n = 1, 2, 3, ... This will be a constant only for geometric sequences.
No. Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one. A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
Yes, that's what a geometric sequence is about.
A harmonic sequence is a sequence of numbers in which the reciprocal of each term forms an arithmetic progression. In other words, the ratio between consecutive terms is constant when the reciprocals of the terms are taken. It is the equivalent of an arithmetic progression in terms of reciprocals.
You mean what IS a geometric sequence? It's when the ratio of the terms is constant, meaning: 1, 2, 4, 8, 16... The ratio of one term to the term directly following it is always 1:2, or .5. So like, instead of an arithmetic sequence, where you're adding a specific amount each time, in a geometric sequence, you're multiplying by that term.
yes