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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 12th term of a geometric sequence in which the common ratio is 2 and the first term is 12?
36
What is the sixth term of a geometric sequence when the first term is 1 and the common ratio is -4?
-1,024
What is the nth term of the geometric sequence 4 8 16 32 ...?
The given sequence is a geometric sequence where each term is multiplied by 2 to get the next term. The first term (a) is 4, and the common ratio (r) is 2. The nth term of a geometric sequence can be found using the formula ( a_n = a \cdot r^{(n-1)} ). Therefore, the nth term of this sequence is ( 4 \cdot 2^{(n-1)} ).
What is the common ratio sequence of 3?
A common ratio sequence, or geometric sequence, is defined by multiplying each term by a fixed number, known as the common ratio. If the first term of the sequence is 3 and the common ratio is, for example, 2, the sequence would be 3, 6, 12, 24, and so on. If the common ratio were instead 1/2, the sequence would be 3, 1.5, 0.75, 0.375, etc. Essentially, the sequence can vary widely based on the chosen common ratio.
What is the 7th term in the geometric sequence whose first term is 5 and the common ratio is -2?
Find the 7th term of the geometric sequence whose common ratio is 1/2 and whose first turn is 5
What is the 12th term of a geometric sequence in which the common ratio is 2 and the first term is 12?
36
What is the sixth term of a geometric sequence when the first term is 1 and the common ratio is -4?
-1,024
What is the sixth term of a geometric sequence when the first term is 7 and the common ratio is 1.1?
11.27357
What is the 12th term in a geometric sequence that has a first term of 6 and a common ratio of 3?
It is 1062882.
What does Geometric Series represent?
A geometric series represents the partial sums of a geometric sequence. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r)
Is 2 10 50 250 1250 geometric?
This is a geometric sequence of the form a, ar, ar^2, ar^3, ... where a is the first term and r is the common ratio.In our case, the first term a = 2, and the common ratio r = 5.The nth term of such a sequence isan = a r^(n -1).
How do you find the given term in a geometric sequence?
nth term Tn = arn-1 a = first term r = common factor
What is the 7th term of a geometric sequence in which the common ration is negative one half and the first term is 4096?
4096-20481024-512256-12864
What is the fifth term of the geometric sequence?
It is a*r^4 where a is the first term and r is the common ratio (the ratio between a term and the one before it).
The sum to three terms of geometric series is 9 and its sum to infinity is 8. What could you deduce about the common ratio. Why. Find the first term and common ratio?
The geometric sequence with three terms with a sum of nine and the sum to infinity of 8 is -9,-18, and 36. The first term is -9 and the common ratio is -2.
How do geometric sequences apply to a bouncing ball?
The ball does not return to its initial height after bouncing. So the height it reaches after the first bounce will be a fraction of the initial height, etc. This is a geometric sequence with common ratio 5/8.
