② accumulation method: the recursive formula is an+ 1=an+f(n), and f(n) can be summed.

③ Multiplication: The recursive formula is an+ 1/an=f(n), and f(n) is integrable.

④ Construction method: transforming non-arithmetic progression and geometric progression into related arithmetic progression.

⑤ Dislocation subtraction: used to form a sequence consisting of arithmetic × equal proportion: for example, an = n 2n.

A series of numbers arranged in a certain order are called series, and the nth item of series {an} is expressed by a specific formula (including parameter n), which is called the general term formula of series. This is like the analytic expression of a function. Substitute a specific value of n, and you can know the corresponding an? The value of the item. The solution of the general term formula of sequence is usually obtained by transforming its recursive formula many times.

Extended data

Arithmetic progression's other inferences:

① Sum = (the first item+the last item) × the number of items ÷ 2;

② Number of items = (last item-first item) ÷ tolerance+1;

③ The first term =2x and the number of terms-the last term or the last term-tolerance× (the number of terms-1);

④ The last item =2x and the number of items-the first item;

(5) the last item = the first item+(item number-1)× tolerance;

⑥2 (sum of the first 2n terms and-the first n terms) = sum of the first n terms and+the first 3n terms and-the first 2n terms.