If the common ratio is negative then the points are alternately positive and negative. While their absolute values will lie on an exponential curve, an oscillating sequence will not lie on such a curve,
A sequence is geometric if each term is found by mutiplying the previous term by a certain number (known as the common ratio). 2,4,8,16, --> here the common ratio is 2.
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 10.
The common ratio.
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
No, geometric, common ratio 2
Yes, all geometric sequences are a specific type of exponential sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio, which can be expressed in the form ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term and ( r ) is the common ratio. This structure aligns with the definition of exponential functions, where the variable is in the exponent. However, not all exponential sequences are geometric, as they can have varying bases or growth rates.
The sequence is neither arithmetic nor geometric.
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.
A single number does not constitute a sequence.
A single number does not constitute a sequence.
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 answer is 4
A static sequence: for example a geometric sequence with common ratio = 1.
Not sure about this question. But, a geometric sequence is a sequence of numbers such that the ratio of any two consecutive numbers is a constant, known as the "common ratio". A geometric sequence consists of a set of numbers of the form a, ar, ar2, ar3, ... arn, ... where r is the common ratio.
A sequence is geometric if each term is found by mutiplying the previous term by a certain number (known as the common ratio). 2,4,8,16, --> here the common ratio is 2.
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 10.
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