1, where a 1 is the first term, an is the nth term, and n is the number of terms. Derivation of this formula: First, we know that arithmetic progression's general formula is: an = a1+(n-1) D. Substitute the general formula into the first n summation formulas: Sn=(a 1+a2+a3+...+an)/2.
2. The result is: Sn=n/2×(a 1+an). Using this formula, the sum of the first n terms of arithmetic progression can be calculated quickly, especially when the sum of multiple terms needs to be calculated, the answer can be obtained by substituting the first term, the tolerance and the number of terms.
Arithmetic progression is a concept.
1, arithmetic progression is a special series, and its characteristic is that the difference between each term and its previous term is equal to a constant. This series is widely used in mathematics and real life. Definition: If a series starts from the second term, the difference between each term and its previous term is equal to the same constant, which is called tolerance, and this series is called arithmetic progression. This tolerance is usually represented by the letter d.
2. The nature of arithmetic progression: the difference between any item of arithmetic progression and its previous item is equal to tolerance D. The difference between any two items of arithmetic progression and its previous item is also equal to tolerance D. In arithmetic progression, starting from the second item, each item is the average of its previous two items. In arithmetic progression, starting from the second item, every other item is odd or even.
3. The application of arithmetic progression in real life: date calculation: for example, today is August 15, then August 16 is August 15 plus 1 day, which is the second item in arithmetic progression; August 17 is August 15 plus 2 days, which is the third item in arithmetic progression, and so on.
4. Savings business: If banks distribute the principal and interest equally within a certain period, a arithmetic progression can be formed. For example, if you deposit a certain amount every month, the total amount after one year is the sum of the original principal plus the monthly interest. This is a arithmetic progression.
5. Temperature change: In meteorology, temperature change often forms arithmetic progression. For example, the daily temperature may gradually increase or decrease with the passage of time, forming a arithmetic progression. Musical scale: The scale in music is also a arithmetic progression. For example, the white keys on the piano are arranged in the order of C, D, E, F, G, A and B from left to right to form a arithmetic progression.