20 16 Necessary Mathematical Formula for College Entrance Examination (1)
The solution of the general formula:
(1) Constructing geometric series: As long as there are recursive formulas about the latter term and the former term, the formula for finding the general term of geometric series can be constructed;
(2) Constructing arithmetic progression: When the recursive formula cannot construct geometric progression, constructing arithmetic progression;
(3) Recursion: that is, according to the corresponding law between the latter term and the former term, the corresponding formula is derived from the former term.
Common methods for finding general terms by known recursive formulas;
① when a 1 = a and an+ 1 = qan+b are known, the key is to determine the undetermined coefficient λ, so that an+ 1 +λ=q(an+λ) can be obtained.
② When A 1 = a and an = an- 1+f (n) (n ≥ 2) are known, when an is found, it is solved by the accumulation method, that is, an = a1+(A2-A1)+(A3-A2)
③ When A 1 = a and an = f (n) an- 1 (n ≥ 2) are known, when an is found, it is solved by iterative method.