1. Observe the law of the series: first observe the first few items of the series to see if there is any law between them. For example, if the first few items in the sequence are 2, 5, 8, 1 1, ..., we can find that each item is 3 more than the previous one. Therefore, the tolerance is 3 and the first term is 2.
2. Use formulas: For arithmetic series, formulas can be used to determine the first term and tolerance. The general formula of arithmetic progression is an=a 1+(n- 1)d, where an represents the nth term, a 1 represents the first term and d represents the tolerance. The first item and tolerance can be solved by knowing an item in the series and its serial number.
3. Using recursive relation: Some series can determine the first term and tolerance through recursive relation. Recursive relation means that each term in the exponential sequence is related to one or more previous terms. By observing the recurrence relation, the first term and tolerance can be obtained.
4. Use the properties of series: Some series have specific properties, through which the first term and tolerance can be determined. For example, each term in a geometric series is the previous term multiplied by a constant. By observing this constant, we can determine the common ratio and then determine the first term.
5. Use mathematical reasoning: Sometimes, it is necessary to determine the first term and tolerance through mathematical reasoning. This may involve some mathematical concepts and theorems, such as algebra, geometry, probability and so on. The first term and tolerance can be obtained by analyzing the characteristics and properties of the sequence and making logical reasoning.
In short, to determine the first term and tolerance of series, we need to carefully observe the law of series, and use formulas, recursive relations, the properties of series and mathematical reasoning to analyze and calculate. Through these methods, we can accurately determine the first term and tolerance of the series, thus solving the related series problems.