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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 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 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.
How do you work out the 20th term of a sequence?
To find the 20th term of a sequence, first identify the pattern or formula that defines the sequence. This could be an arithmetic sequence, where each term increases by a constant difference, or a geometric sequence, where each term is multiplied by a constant factor. Once the formula is established, substitute 20 into the formula to calculate the 20th term. If the sequence is defined recursively, apply the recursive relation to compute the 20th term based on the previous terms.
How do you find the 100th number in a sequence?
To find the 100th number in a sequence, first identify the pattern or rule governing the sequence. This could be arithmetic, geometric, or another type of progression. Once the formula or pattern is established, you can apply it to calculate the specific term for the 100th position. For example, in an arithmetic sequence defined by (a_n = a_1 + (n-1)d), you would substitute (n = 100) to find the desired term.
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.
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.
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.
How do you work out the 20th term of a sequence?
To find the 20th term of a sequence, first identify the pattern or formula that defines the sequence. This could be an arithmetic sequence, where each term increases by a constant difference, or a geometric sequence, where each term is multiplied by a constant factor. Once the formula is established, substitute 20 into the formula to calculate the 20th term. If the sequence is defined recursively, apply the recursive relation to compute the 20th term based on the previous terms.
Could a cross be a geometric shape?
no
How do you find the 100th number in a sequence?
To find the 100th number in a sequence, first identify the pattern or rule governing the sequence. This could be arithmetic, geometric, or another type of progression. Once the formula or pattern is established, you can apply it to calculate the specific term for the 100th position. For example, in an arithmetic sequence defined by (a_n = a_1 + (n-1)d), you would substitute (n = 100) to find the desired term.
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.
