1. Determine the tolerance: First, you need to determine the tolerance of arithmetic progression, which is the difference between two adjacent items. Tolerance can be determined by observing the law of sequence or according to the conditions given by the topic.
2. Use the general formula: arithmetic progression's general formula is an=a 1+(n- 1)d, where a 1 represents the first term, d represents the tolerance and n represents the number of terms. By substituting the known conditions, the value of the unknown term can be found.
3. Using the formula of the first n terms: The formula of the first n terms in arithmetic progression is Sn=n(a 1+an)/2, where Sn represents the sum of the first n terms and N represents the number of terms. By substituting the known conditions, the value of the sum of the first n items can be obtained.
4. Utilization properties: arithmetic progression has some special properties. For example, even and odd terms in arithmetic progression constitute arithmetic progression respectively, and the sum of any two terms in arithmetic progression is equal to the third term multiplied by the number of terms plus one. These properties can be used to simplify the calculation process.
5. Using recurrence relation: arithmetic progression's recurrence relation is an+ 1-an=d, through which the unknown term in arithmetic progression can be solved.
6. Graphic method: Mark the value of arithmetic progression on the coordinate axis to get a straight line. By observing the slope and intercept of a straight line, the tolerance and the first term can be obtained.
7. Use grouping summation: When there are many items in arithmetic progression, the series can be divided into several groups, each group has the same tolerance, and then summed separately and then added, which can simplify the calculation process.
8. Use symmetry: arithmetic progression has symmetry, that is, symbols appear alternately. This property can be used to simplify the calculation process.
9. Using multiple relation: each term in arithmetic progression is a multiple of the previous term plus a constant, which can be used to solve the unknown term.
10. Using the inverse proportional relation, each term in arithmetic progression can be expressed as a constant multiple of the previous term plus a constant, and the unknown term can be solved by using this relation.