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Q: What situations could be modeled by a geometric sequence?
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A sequence of numbers that follows a rule is a what?

It is a sequence of numbers. That is all. The sequence could be arithmetic, geometric, harmonic, exponential or be defined by a rule that does not fit into any of these categories. It could even be random.


What is Nth term of a non linear sequence?

It is not possible to answer the question since a non linear sequence could be geometric, exponential, trigonometric etc.


Can a sequence of numbers be both geometric and arithmetic?

Yes, it can both arithmetic and geometric.The formula for an arithmetic sequence is: a(n)=a(1)+d(n-1)The formula for a geometric sequence is: a(n)=a(1)*r^(n-1)Now, when d is zero and r is one, a sequence is both geometric and arithmetic. This is because it becomes a(n)=a(1)1 =a(1). Note that a(n) is often written anIt can easily observed that this makes the sequence a constant.Example:a(1)=a(2)=(i) for i= 3,4,5...if a(1)=3 then for a geometric sequence a(n)=3+0(n-1)=3,3,3,3,3,3,3and the geometric sequence a(n)=3r0 =3 also so the sequence is 3,3,3,3...In fact, we could do this for any constant sequence such as 1,1,1,1,1,1,1...or e,e,e,e,e,e,e,e...In general, let k be a constant, the sequence an =a1 (r)1 (n-1)(0) with a1 =kis the constant sequence k, k, k,... and is both geometric and arithmetic.


What is the common ratio of the geometric sequence whose second and fourth terms are 6 and 54 respectively?

It could be -3 or +3.


What is a rectangular number sequence?

A rectangular number sequence is the sequence of numbers of counters needed to construct a sequence of rectangles, where the dimensions of the sides of the rectangles are whole numbers and change in a regular way. The individual sequences representing the sides are usually arithmetic progressions, but could in principle be given by difference equations, geometric progressions, or functions of the dimensions of the sides of previous rectangles in the sequence.


What is the 9th term of the following geometric sequence Enter a whole number - 7 -21 63?

The sequence, -7, -21, 63 could be generated by Un = 49n2 - 161n + 105 so when n = 9 the term would be 2625.


Is this sequence arithmetic or geometric 12 48 ... 192?

It could be either. The answer depends on how many terms if any are between 48 and 192.


Could a cross be a geometric shape?

no


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 you find the next term of a sequence number?

The first step is to find the sequence rule. The sequence could be arithmetic. quadratic, geometric, recursively defined or any one of many special sequences. The sequence rule will give you the value of the nth term in terms of its position, n. Then simply substitute the next value of n in the rule.


What is a sequence that could result from an inversion of the sequence GAGACATT?

An inversion of the sequence GAGACATT could result in the sequence CATTCTC. This is because an inversion would flip the sequence and reverse its order.


How could you have modeled 624 without using tens?

6 hundred and 24 ones