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In a geometric sequence where the terms always increase, the common ratio ( r ) must be greater than 1. This means that each term is obtained by multiplying the previous term by this positive ratio. For example, if the first term is ( a ) and the common ratio is ( r ), the sequence would look like ( a, ar, ar^2, ar^3, \ldots ) with each term growing larger than the last. Thus, the sequence exhibits exponential growth as long as the common ratio remains above 1.
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Do the terms of a geometric sequence increase as it proceeds?
yes
Is geometric sequence a sequence in which each successive terms of the sequence are in equal ratio?
Yes, that's what a geometric sequence is about.
What does geometric sequence?
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.
What is a geometric sequence that has 5 terms and alternating?
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.
What is the answer if you insert 3 terms between 2 and 32 by geometric sequence?
The terms are: 4, 8 and 16
DO the terms in a geometric sequence always increase?
FALSE (Apex)
In a geometric sequence where r and gt 1 the terms always increase.?
No, they do not. If the first term is negative, they always decrease.
Do the terms of a geometric sequence increase as it proceeds?
yes
Is geometric sequence a sequence in which each successive terms of the sequence are in equal ratio?
Yes, that's what a geometric sequence is about.
Descending geometric sequence?
A descending geometric sequence is a sequence in which the ratio between successive terms is a positive constant which is less than 1.
In what sequence are all of the terms the same?
A static sequence: for example a geometric sequence with common ratio = 1.
What does geometric sequence?
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.
In a geometric sequence the between consecutive terms is constant.?
Ratio
find the next two terms in geometric sequence 2,6,18,54,162,486,1458?
It is 4374
What is the difference between succeeding terms called?
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.
What is the answer if you insert 3 terms between 2 and 32 by geometric sequence?
The terms are: 4, 8 and 16
Is the sequence 2 3 5 8 12 arithmetic or geometric?
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.
