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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.
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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.
