What are the basic question types of mathematical sequences, and what are the 19 classic question ty

Equal difference seriesSummary of problem-solving skills and questions:

The sum of the number series is the sum of the numbers that are sorted according to a certain rule. Finding SN is essentially a general formula, and attention should be paid to understanding its meaning. There is a formula for the common way to get hungry.

Dislocation subtraction, reverse order addition, grouping, splitting, mathematical induction.

Generalization, merger summing, but the general way is to memorize the way in the figure above.

The number series is the key content of analytic geometry in high school, is the basis for learning advanced mathematics subjects, and occupies a key position in the college entrance examination (college entrance examination) and various mathematics subject competitions.

In addition to the summation formula, the summation of most sequences requires a certain amount of skill, which is some special sequences, which should be memorized separately.

The solution process should pay attention to the use of the general method and the clever method, the first choice is to use the clever method, and if it is really bad, you can use the general method to generate A1 and D, and then solve it.

The use of key formulas, secretary formulas, application, and solving.

to recursive formulas.

It is necessary to strengthen training and make perfect.

Method 2 is simpler, so be sure to grasp it.

Simplify it first, and then eliminate the split items, and it's simple.

Dislocation and subtraction should be emphasized, the last two items equivalent to sn should be written, multiplied by the common ratio, misplaced writing, subtraction, the last term is preceded by a minus sign, and the part between is summed by the number series formula, and then simplified, and then the coefficient in front of sn is removed.

The types of number series questions and how to solve them are as follows:1. Equal difference series.

This kind of test is to find the pattern by making the original number series worse, sometimes you can find the pattern by making a difference, and sometimes you need to make a second difference to the new number series.

Question type characteristics: The original data is generally monotonic, and the data does not change much.

2. and sequences.

This kind of test is to find the law by making the original number series sum, which can be two numbers to do the sum, or three numbers to do the sum. Usually the obtained sum is either related to the next number, or the obtained sum will form a new sequence.

Characteristics of the question type: The original data is monotonicity, and when you can't find a pattern when you can't find a pattern, you can try to do sum; The original data itself is not monotonicity and the change range is not large, so we directly try to do sum.

Number Sequence Problem Solving Skills:1. There are many items in the number series, and priority is given to combining the number series.

2. If there are characteristic numbers in the sequence, give priority to the characteristic numbers.

3. The increase in numbers is getting bigger and bigger, and priority is given to the product and multiple square angles.

4. The number series increases or decreases, but the amplitude is moderate, and the difference between two adjacent items is preferred.

5. The multiple relationship between the items of the series is obvious, and the quotient or product series and its variants are considered.

6. While analyzing the stem numbers, it is necessary to combine the numbers in the options to further judge the rules of the number series.

The common methods of the number series include formula method, dislocation subtraction method, reverse order addition method, grouping method, split term method, mathematical induction method, general term reduction, and union summing.

Accumulation. The recursive formula is.

and f(n) can be summed;

Multiplication. The recursive formula is.

and f(n) can find the product of the alluvial key;

Construct. Convert non-proportional series and proportional series into related proportional series.

1.Perform the operation appropriately to determine the deformation number blindness.

2.Reciprocal transformation method.

3.Pending coefficient method aThe recursive formula is an+1 = p*an + q (p, q is constant), and you can construct a recursive number column Proportional series with p as the common ratio.

4.The recursive formula of the eigenroot method is an+1 = a*an+b) c*an+d) (a,b,c, potato empty d is constant) so that an+1 = an = x, and the original formula is x = ax+b) cx+d)(1) If the same real root x0 is solved, the number column can be constructed as an equal difference series.

High school math sequence.

Question Type:

1. Equal difference series and proportional series.

Question Type 1] The connection between the difference series and the proportional series, Question Type 2] The combination of "the first n terms and the sn term and the general term an", the commonly used formula for finding the general term, [Question Type 3] The formula of the middle term and the maximum value (the sequence has the property of a function), 2. The sum of the first n terms of the series.

Question Type 1] Formula Method, Question Type 2] Group Summation Method, Question Type 3] Split Elimination Method, Question Type 4] Dislocation Subtraction Method, Question Type 5] Merging Sum Method, Question Type 6] Accumulation (Multiplication) Method and Other Methods: Induction, Conjecture, Proof; The summation of the periodic series, etc., and the general term formula of the series.

Question Type 1] Periodic Sequence, Question Type 2] The recursive formula is an =an+f(n), find the general term, [Question Type 3] The recursive formula is an =f(n)an, find the general term, [Question Type 4] The recursive formula is an = pan+q (where p and q are constants, pq(p-1)≠0), find the general term, question type 5] Construction method: 1) Construct an equal difference series or proportional series, [Question Type 6] Construction method: 2) Construct difference and sum formula, [Question Type 7] Construction method:

3) Constructing quotient and product, [Question Type 8] Constructing method: 4) Constructing logarithm or reciprocal formula, [Question Type 9] Inductive conjecture proof.