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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 an
It 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)=3,3,3,3,3,3,3
and 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 =k
is the constant sequence k, k, k,... and is both geometric and arithmetic.
What else can I help you with?
What are four numbers that make both an arithmetic and geometric series?
1,2,4, and 8.
How do you calculate the geometric mean?
The geometric mean, by definition, is the nth root of the product of the n units in a data set. For example, the geometric mean of 5, 7, 2, 1 is (5x7x2x1)1/4 = 2.893 Alternatively, if you log transform each of the individual units the geometric will be the exponential of the arithmetic mean of these log-transformed values. So, reusing the example above, exp[ ( ln(5)+ln(7)+ln(2)+ln(1) ) / 4 ] = 2.893 I agree with the above BUT... with two numbers, a geometric mean is the square root of the product (result of multiplication) of the two numbers while the arithmetic mean is half of the sum of the two numbers. For example, 2 and 8. The geometric mean is 2*8 = 16, sqrt(16) = 4. The arithmetic mean is (2+8)/2 = 5. Both give a number somewhere between those that contribute AND when the numbers are the same, both will agree. For 6 and 6, sqrt(36) = 6, 12/2 = 6. In other cases, they have different properties which make them advantageous in different places. BUT you should think of the two has having the same goal and being very similar in form (just turning addition to multiplication and multiplication to exponentiation). The earlier answer is better because it shows the generalization beyond two numbers (that is, when you have four numbers, you will multiply them all together and take the 4th root, rather than the square root), I added this to draw the similarity to a conventional mean and give an example that you could follow in your head. (Just wondering, why is it useful to show that for exponents multiplication becomes addition? -- I am not following the relevance to a geometric mean.)
What is the general rule for the arithmetic sequence 15 12 9 6?
There are two ways to say the general rule. They both mean exactlythe same thing, and they both generate the same sequence:1). Starting with 15, each new term is 3 less than the one before it.2). The nth term of the sequence is [ 18 - 3n ] or [ 3 times (6 - n) ].
What geometric shape has 11 sides?
A geometric shape that has 11 sides is called a "hendecagon" or "undecagon." Both terms are acceptable.
Will 0.54732814 produce a rational number when multiplied by 0.5?
The product of two rational numbers is a rational number. All decimal numbers that terminate or end with a repeating sequence of digits are rational numbers. As both 0.54732814 (as written) and 0.5 are terminating decimals, they are both rational numbers. As 0.54732814 is a rational number and 0.5 is a rational number, their product will also be a rational number.
What is the sequence of numbers that are both geometric and arithmetic?
It is called arithmetico-geometric sequence. I have added a link with some nice information about them.
Is -4 -8 -16 -32 arithmetic geometric both or neither?
It is a geometric sequence.
How can a sequence be both arithmetic and geometric?
A sequence can be both arithmetic and geometric if it consists of constant values. For example, the sequence where every term is the same number (e.g., 2, 2, 2, 2) is arithmetic because the difference between consecutive terms is zero, and it is geometric because the ratio of consecutive terms is also one. In such cases, the sequence meets the criteria for both types, as both the common difference and the common ratio are consistent.
What are four numbers that make both an arithmetic and geometric series?
1,2,4, and 8.
How are arithmetic and geometric sequences similar?
Arithmetic and geometric sequences are similar in that both are ordered lists of numbers defined by a specific rule. In an arithmetic sequence, each term is generated by adding a constant difference to the previous term, while in a geometric sequence, each term is produced by multiplying the previous term by a constant factor. Both sequences can be described using formulas and have applications in various mathematical contexts. Additionally, they both exhibit predictable patterns, making them useful for modeling real-world situations.
What is the two kinds of sum?
The two kinds of sums typically refer to the arithmetic sum and the geometric sum. An arithmetic sum is the total of a sequence of numbers where each term increases by a constant difference, while a geometric sum involves a sequence where each term is multiplied by a constant ratio. Both types of sums can be expressed using specific formulas to calculate their totals efficiently.
What is geometric and arithmetic?
They are both adjectives. The first relates to geometry and the second to arithmetic.
Properties and limitations of geometric mean?
In a given sequence, there are two possible means calculatable: Arithmetic Mean, and Geometric Mean. The arithmetic mean, as we all know, is calculated from the sum of all the numbers divided by how many numbers there are: Sumn/n. The Geometric sum is calculated by multiplying all the numbers within the sequence together and taking the nth root of this value: (Productn)(1/n).In a geometric series, N(i)= a(ri), the geometric mean is found to be a(rn-1), where n is the number of elements within the series. this decreases or increases exponentially depending on the r value. If r1, increasing.Limitation Of Geometric Mean are:-1) Geometric mean cannot be computed when there are both negative and positive values in a series or more observations are having zero value.2)Compared to Arithmetic Mean this average is more difficult to compute and interpret.-Iwin
How do you get the geometric mean of two numbers?
you add both of the two numbers together then divide the added number by the quantities of the items, in this case Two numbers and get the result. * * * * * The above is the arithmetic mean, which is quite different from the geometric mean. To get the geometric mean of n positive numbers, you multiply (not add) them together and take the nth root of the answer.
Is a geometric progression a quadratic sequence?
A geometric sequence is : a•r^n while a quadratic sequence is a• n^2 + b•n + c So the answer is no, unless we are talking about an infinite sequence of zeros which strictly speaking is both a geometric and a quadratic sequence.
How do you get the mean of the number?
you add both of the two numbers together then divide the added number by the quantities of the items, in this case Two numbers and get the result. * * * * * The above is the arithmetic mean, which is quite different from the geometric mean. To get the geometric mean of n positive numbers, you multiply (not add) them together and take the nth root of the answer.
What are two similarities between the base five arithmetic and clock five arithmetic?
base five and clock arithmetic both use whole numbers. and they both use place value to calculate.
