This sequence is puzzling, particularly because the steps initially increase in magnitude; and yet the sequence then takes three steps just to fall from 30 to 24, a surprise which runs counter to our intuitions. Alternative reasons for this odd behaviour could be: * The sequence isn't a straightforward function, but rather involves some recursive relationship between terms. * The series is an elementary function, but it isn't using the counting numbers as its input. It might be based on the prime numbers, for instance. * The individual digits of each term are manipulated to determine the next. * The sequence is based upon a constant, like pi or e. * It involves geometric / trigonometric ideas. * The sequence is not using the decimal system. * The sequence isn't purely mathematical - it makes reference to some independent external data or sequence. I list all these exotic possibilities for one reason: there will be a great many different rules that could produce such a succession of terms. Some of them will be more elegant than others, so it's a good idea to keep an open mind. But here is the more mundane hypothesis that I will work with: * The sequence is confusing because it is produced by a function that is neither linear or quadratic but of a higher degree. If you sketch a graph of the sequence*, it is absolutely clear that it cannot possibly be a quadratic function, because it is neither concave nor convex, but first one and then the other. What this means in mathematical terms is that the rate of change of gradient (the second differential) undergoes a sign change somewhere. For this to happen, d2y/dx2 must be variable, i.e. it is a function of degree 1 or greater. It follows that dy/dx must be at least degree 2, and the actual function must have at least degree 3. In other words, the function could be a cubic of form ax3 + bx2 + cx + d Normally cubic sequences can be identified at once because the third difference (the difference of the difference of the difference) is constant. This method requires 5 consecutive terms however, and we were only given three. To pin down the function that we are dealing with, we would need to solve for the coefficients a, b, c and d: four unknowns to find. It happens that we have been given 4 terms in the sequence, therefore we can form four equations and solve for four unknowns. Actually, that is why this approach is rather disappointing and lacking in elegance. If you are given a number n terms of a sequence, then it is always possible to find a valid rule using a polynomial of degree n-1. For instance, if you gave me the first twenty terms of the Fibonacci series, I could find a rule that worked using powers of x up to x19, but it wouldn't be the best answer. Still, I can't see a better way forward, so let's proceed with our cubic function. We have four simultaneous equations: a + b + c + d = 45 a + b + c + d = 45a + b + c + d = 39 8a + 4b + 2c + d = 39 a + b + c + d = 39 27a + 9b + 3c + d = 30 a + b + c + d = 24 216a + 36b + 6c + d = 24 The way to solve them is to rearrange an equation to get one variable in terms of all the others, and then to substitute for it in the remaining equations. Repeating this tedious process will eventually eliminate all but one variable: the solution for this one variable can then be used to find the value of the others. To cut a long story short, the solution is: a = 13/20 b = -108/20 c = 113/20 d = 882/20 We can write a function giving y in terms of x that applies to the sequence: y = [13x3 - 108x2 + 113x + 882] / 20 As predicted, it is far from pretty, and I suspect there was some simpler rule that you were meant to find. Still, this one is perfectly valid. It gives the missing terms as 21.9 andf 18.6, in that order. *Plotting the given values against their positions in the sequence, y against x.
There is no formula for prime numbers. They form a random sequence.
You find the first 20 prime numbers and add them together. There is no formula for generating a sequence of prime numbers and so none for the series of their sums.You find the first 20 prime numbers and add them together. There is no formula for generating a sequence of prime numbers and so none for the series of their sums.You find the first 20 prime numbers and add them together. There is no formula for generating a sequence of prime numbers and so none for the series of their sums.You find the first 20 prime numbers and add them together. There is no formula for generating a sequence of prime numbers and so none for the series of their sums.
There is no formula that will sum n even numbers without further qualifications: for example, n even numbers in a sequence.
You didn't say the series (I prefer to use the word sequence) of even numbers are consecutive even numbers, or even more generally an arithmetic sequence. If we are not given any information about the sequence other than that each member happens to be even, there is no formula for that other than the fact that you can factor out the 2 from each member and add up the halves, then multiply by 2: 2a + 2b + 2c = 2(a + b + c). If the even numbers are an arithmetic sequence, you can use the formula for the sum of an arithmetic sequence. Similarly if they are a geometric sequence.
In principle, only by comparing the chemical formula for the compound with the formulas of ions known to be polyatomic to determine whether the sequence of letters and subscript numbers (if any) in any part of the chemical formula corresponds to the sequence of letters and subscript numbers in the formula of a know polyatomic ion.
It is not possible to explain because you have not specified the nature of the sequence. A sequence can be an arithmetic, or geometric progression, increasing or decreasing. Or it can be a polynomial or power progression, again increasing or decreasing. Or it can be a sequence of random numbers.
Question is not very clear about the context of word 'sequence' here. If I am to select 4 numbers out of four and arrange them in order then there are 4!*8C4 = 1680 different sequences possible. If the word sequence refers to some arithmetic sequence or geometric sequence, then counting is going to change for sure.
8, if it is the Fibonacci sequence; 7, if it the sequence of non-composite numbers (1 and primes); there are other possible answers.
The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.The formula for the sum of an arithmetic sequence is ((first number) + (last number)) x (how many numbers) / 2, in this case, (1 + 100) x 100 / 2.
There are no numbers before the sequence!
the first 4 terms of the sequence which has the nth term is a sequence of numbers that that goe together eg. 8,12,16,20,24 the nth term would be 4n+4
There is a proof that there is no such formula for generating all the prime numbers. Best, TSA
It is possible if you define some arbitrary sequence, to decide which number comes "after" which other number. There is no "natural" sequence, as in the case of integers; to be more precise, you can't use the ordering defined by the "less-than" operator as such a sequence: between any two different rational numbers, there are additional rational numbers.
There are infinitely many possible number sequences, and infinitely many numbers which can appear in those sequences. Any and every number can appear in a number sequence.
The set of odd numbers is an arithmetic sequence. Let say that the sequence has n odd numbers where the first term is a1 and the last one is n. The formula to find the sum on nth terms for an arithmetic sequence is: Sn = (n/2)(a1 + an) or Sn = (n/2)[2a1 + (n - 1)d] where d is the common difference that for odd numbers is 2. Sn = (n/2)(2a1 + 2n - 2)
it means a sequence of numbers and letters to send you to a specific location. (I had this question as homework at school)
A number derived by applying a formula to a sequence of numbers which will independently validate the authenticity of an alternatively derived result.
It would contain of all the number from 1000 to 9998 leaving 9 numbers.
This is called a sequence and if we add the numbers in that sequence it is called a series.
An arithmetic sequence is a list of numbers which follow a rule. A series is the sum of a sequence of numbers.
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
They are a sequence of numbers and each sequence has a term number.