1,2,4, and 8.
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.
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.)
A geometric shape that has 11 sides is called a "hendecagon" or "undecagon." Both terms are acceptable.
The answer is two arithmetic sequences, both with a common difference of 3, alternating with one another, where the second series is greater than the first by the value of 2*A(0), ie twice the starting value.
if there are 2 medians then take them both and find the average. Like if the numbers are 1,2,3,4,5,6 the medians are 3 and 4 so you would add them both together and divide by how many numbers there are in this case 2; you would get 7 and then divide that by 2 and get 3.5 so that is the median in this case.
It is called arithmetico-geometric sequence. I have added a link with some nice information about them.
They are both adjectives. The first relates to geometry and the second to arithmetic.
It is a geometric sequence.
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
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.
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.
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.
AP - Arithmetic ProgressionGP - Geometric ProgressionAP:An AP series is an arithmetic progression, a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 3, 5, 7, 9, 11, 13, … is an arithmetic progression with common difference 2. If the initial term of an arithmetic progression is and the common difference of successive members is d, then the nth term of the sequence is given by:and in generalA finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression.The behavior of the arithmetic progression depends on the common difference d. If the common difference is:Positive, the members (terms) will grow towards positive infinity.Negative, the members (terms) will grow towards negative infinity.The sum of the members of a finite arithmetic progression is called an arithmetic series.Expressing the arithmetic series in two different ways:Adding both sides of the two equations, all terms involving d cancel:Dividing both sides by 2 produces a common form of the equation:An alternate form results from re-inserting the substitution: :In 499 AD Aryabhata, a prominent mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave this method in the Aryabhatiya (section 2.18) .[1]So, for example, the sum of the terms of the arithmetic progression given by an = 3 + (n-1)(5) up to the 50th term isGP:A GP is a geometric progression, with a constant ratio between successive terms. For example, the series is geometric, because each successive term can be obtained by multiplying the previous term by 1 / 2.Geometric series are one of the simplest examples of infinite series with finite sums, although not all of them have this property. Historically, geometric series played an important role in the early development of calculus, and they continue to be central in the study of convergence of series. Geometric series are used throughout mathematics, and they have important applications in physics, engineering, biology, economics, computer science, queuing theory, and finance.
base five and clock arithmetic both use whole numbers. and they both use place value to calculate.
Let the sum of series a1,.., an = A. Since ai >0. Then the maximum possible product of a1,..,an is = (A/n)n. This result basically comes the relation between the arithmetic mean and geometric mean of n positive numbers. A/n >= (a1...an)(1/n). The equality case of the above relation gives the maximum product (by raising the power by n on both sides).
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.)
Not usually. Given numbers a and b, the mean or average is (a + b)/2 but the geometric mean is sq rt (a X b). If both a and b equal 1, the results are the same.