Give a sequence how to quickly know its general formula, is there a rule I feel that it needs more feeling than painting color, that is, to make up the number. Although it can be made, it always takes some time. Why?

Give a sequence how to quickly know its general formula, is there a rule I feel that it needs more feeling than painting color, that is, to make up the number. Although it can be made, it always takes some time. Why?

If the sequence is an arithmetic sequence, its general term a = a + (n-1) d, where a is the first term of the sequence and D is the arithmetic of the sequence. If the sequence is an equal ratio sequence, its general term a = a * q ^ (n-1), where q is the equal ratio of the sequence

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