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Six methods of finding the general term by recursive formula
Six methods of finding the general term by recursive formula: arithmetic progression and geometric progression have the general term formula; Accumulation method; Cumulative multiplication; Structural method; Dislocation subtraction.

A series of numbers arranged in a certain order is called a series, and the nth item of the series {an} is expressed by a specific formula, which is called the general term formula of the series.

Accumulation method: the recursive formula is an+ 1=an+f(n), and f(n) can be summed.

Cumulative method: the recursive formula is an+ 1/an=f(n), and f(n) is integrable.

Construction method: Transform non-arithmetic progression and geometric progression into related arithmetic progression.

Dislocation subtraction: used to form a sequence consisting of arithmetic × ratio: for example, an = n 2n.

Iterative method: This problem can also be solved by inductive guessing, but it should be proved by mathematical induction.