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Well, well, well, look who's getting fancy with geometric sequences! When the ratio between consecutive terms is "r," each term is found by multiplying the previous term by "r." So, in simpler terms, if you have a sequence like 2, 4, 8, 16, the ratio between consecutive terms is 2. Math can be sassy too, honey!
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ProfessorIn a geometric sequence, the ratio between consecutive terms is called the common ratio. This common ratio is denoted by the letter "r." To find any term in a geometric sequence, you can use the formula: (a_n = a_1 \times r^{(n-1)}), where (a_n) is the nth term, (a_1) is the first term, (r) is the common ratio, and (n) is the position of the term in the sequence. The common ratio determines how each term is related to the previous one, making geometric sequences a powerful tool in mathematics and various real-world applications.
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Is -1 -36 216 a geometric sequence and what is its ratio?
No it is not.
Is the following sequence arithmetic or geometric and what is the common difference (d) or the common ration (r) the common ratio (r) of the sequence π2π3π22π?
The sequence is neither arithmetic nor geometric.
How can you tell if a infinite geometric series has a sum or not?
The geometric series is, itself, a sum of a geometric progression. The sum of an infinite geometric sequence exists if the common ratio has an absolute value which is less than 1, and not if it is 1 or greater.
Find the common ratio of the following geometric sequence 2.512 11.304 50.868 228.906 1030.077?
Formula for the nth term of general geometric sequence tn = t1 x r(n - 1) For n = 2, we have: t2 = t1 x r(2 - 1) t2 = t1r substitute 11.304 for t2, and 2.512 for t1 into the formula; 11.304 = 2.512r r = 4.5 Check:
What is the common ratio in this sequence 6 12 24 48 96?
The common ratio is 2.
