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Each stair is the same as the one next to it. An arithmetic sequence shows numbers with even spacing (such as 2,4,6 or 5,10,15)
A sequence where a particular number is added to or subtracted from any term of the sequence to obtain the next term in the sequence. It is often call arithmetic progression, and therefore often written as A.P. An example would be: 2, 4, 6, 8, 10, ... In this sequence 2 is added to each term to obtain the next term.
It is the sequence of first differences. If these are all the same (but not 0), then the original sequence is a linear arithmetic sequence. That is, a sequence whose nth term is of the form t(n) = an + b
It looks like the Fibonacci sequence grouped in two terms and up. The next should be 8132134.
You cant solve the next term (next number) in this sequence. You need more terms, because this is either a "quadratic sequence", or a "linear and quadratic sequence", and you need more terms than this to solve a "linear and quadratic sequence" and for this particular "quadratic sequence" you would need more terms to solve nth term, which would solve what the next number is. If this is homework, check with your teacher if he wrote the wrong sum.