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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 geometric sequence in math mean?
A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3. The general form of a geometric sequence can be expressed as ( a_n = a_1 \cdot r^{(n-1)} ), where ( a_1 ) is the first term, ( r ) is the common ratio, and ( n ) is the term number.
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 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.
