![]() Note that as long as you have a finite sequence of numbers it is always possible to find a polynomial that can describe it. ![]() For fourth degree polynomials we would have to look at yet another level of differences. To solve a third degree polynomial the difference between the differences between the differences need to be constant. Sometimes it can be necessary to use polynomials of higher degree than two but the method is essentially the same. To establish the polynomial we note that the formula will have the following form. This tells us that it is possible to describe the sequence as a second degree polynomial but it does not give us any information about how. If we look at the difference between the five initial numbers we find that they are 3 5 7 9 and, as you can see, the differences between these numbers are 2. 2 5 10 17 26… is an example of such a sequence. If it turns out that the difference between the differences is constant it means that the sequence can be described using a second degree polynomial. If neither quotient nor difference is constant it might be a good idea to look at the difference between the differences. This sequence can be described using the exponential formula a n = 2 n. 2 4 8 16… is an example of a geometric progression that starts with 2 and is doubled for each position in the sequence. In a geometric progression the quotient between one number and the next is always the same. ![]() This sequence can be described using the linear formula a n = 3 n − 2. 1 4 7 10 13… is an example of an arithmetic progression that starts with 1 and increases by 3 for each position in the sequence. More information about these formulas here.In an arithmetic progression the difference between one number and the next is always the same. To generate a list of twelve-month names (instead of dates) you can wrap the formulas above in the TEXT function like this: =TEXT(EDATE(DATE(2022,1,1),SEQUENCE(12,1,0)),"mmmm") ![]() To generate a list of 12 dates corresponding to the first day of the month for all months in a year (2022 in this case) you can use SEQUENCE with the DATE and EDATE functions: =EDATE(DATE(2022,1,1),SEQUENCE(12,1,0)) For example, to generate a list of 10 days starting today in columns, you can use SEQUENCE with the TODAY function. For example, the formulas below generate numbers between 1 and 5 in rows and columns: =SEQUENCE(5,1) // returns īecause Excel dates are serial numbers, you can easily use SEQUENCE to generate sequential dates. ![]() The rows and columns arguments control the number of rows and columns that should be generated in the output. The SEQUENCE function takes four arguments: rows, columns, start, and step. It can also be used to generate a numeric array inside another formula, a requirement that comes up frequently in more advanced formulas. The array can be one-dimensional, or two-dimensional, controlled by rows and columns arguments. SEQUENCE can be used on its own to create an array of sequential numbers that spill directly on the worksheet. The SEQUENCE function generates a list of sequential numbers in an array. ![]()
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