The first step is to find the sequence rule. The sequence could be arithmetic. quadratic, geometric, recursively defined or any one of many special sequences. The sequence rule will give you the value of the nth term in terms of its position, n. Then simply substitute the next value of n in the rule.
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You first need to take a good look at the sequence, and figure out the RULE used to calculate each number. There is really no systematic way to do this; some ingenuity may be required.
you must find the pattern of the sequence in order to find the next 50 terms using that pattern and the first part of the sequence given
Well, by definition a "random number sequence" is random; i.e. you cannot find out the next term.However if you're just trying to find the formula for a "number sequence" (not random):1) look at what you have to do to get from one number in the sequence to the next - example the initial difference between the numbers may give a sequence such as "+4, +6, +8, +10", this then gives a sequence of "+2, +2, +2 etc." - this does help to to find out the formula for the sequence.2) write down the "term numbers" (call this "t") above or below the sequance, (i.e. 1st term, 2nd term etc.) and see what you have to do to get from the term number to the sequence number. i.e "3t-1", "t squared minus 3" etc.
Fibonacci sequence
It is a sequence of numbers which is called an arithmetic, or linear, sequence.
From what I know, it is just called "next term in sequence" For a unknown term, just call it the "nth term".