yes
Yes, that's what a geometric sequence is about.
A geometric sequence with 5 terms can alternate by having positive and negative terms. For example, one such sequence could be (2, -6, 18, -54, 162). Here, the first term is (2) and the common ratio is (-3), leading to alternating signs while maintaining the geometric property.
The terms are: 4, 8 and 16
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.
In a geometric sequence, the ratio between consecutive terms is constant. This means that each term can be obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, the ratio is consistently 3, as each term is three times the preceding one. Thus, the defining characteristic of a geometric sequence is this consistent multiplicative relationship between consecutive terms.
FALSE (Apex)
Yes, that's what a geometric sequence is about.
No, they do not. If the first term is negative, they always decrease.
A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.
A static sequence: for example a geometric sequence with common ratio = 1.
A geometric sequence with 5 terms can alternate by having positive and negative terms. For example, one such sequence could be (2, -6, 18, -54, 162). Here, the first term is (2) and the common ratio is (-3), leading to alternating signs while maintaining the geometric property.
Ratio
It is 4374
The difference between succeeding terms in a sequence is called the common difference in an arithmetic sequence, and the common ratio in a geometric sequence.
The terms are: 4, 8 and 16
The sequence 2, 3, 5, 8, 12 is neither arithmetic nor geometric. In an arithmetic sequence, the difference between consecutive terms is constant, while in a geometric sequence, the ratio between consecutive terms is constant. In this sequence, there is no constant difference or ratio between consecutive terms, so it does not fit the criteria for either type of sequence.
un = u0*rn for n = 1,2,3, ... where r is the constant multiple.