Sn is equal to sn = a1n+((n (n-1))/2) d arithmetic progression. Geometric progression Sn=na 1(q= 1), sn = a1(1-q n)/(1-q), and the sequence is defined by a positive integer set (or its finite set). Formula method, arithmetic progression's summation formula is (the first term+the last term) multiplied by the number of terms /2.

The summation of series is the summation of numbers arranged according to certain rules. Finding Sn is essentially a general formula for finding {an}, so we should pay attention to understanding its meaning. Common methods include formula method, dislocation subtraction method, anti-addition method, grouping method, split term method, mathematical induction method, general term reduction method and union term summation method.

Calculation method of serial number of summation formula of arithmetic sequence

Formula method, the sum formula of arithmetic sequence is (first item+last item) * number of items /2. Dislocation subtraction is suitable for the series form in which the general term formula is the multiplication of arithmetic linear functions with equal proportion, and arithmetic geometric progression multiplication. Reverse addition, which is a method used to derive the first n terms and formulas of arithmetic progression.

Grouping method, there is a series, which is neither arithmetic progression nor geometric progression. If this kind of series is properly decomposed, it can be divided into several arithmetic progression, proportional series or ordinary series, and then summed and merged separately. Split term elimination method is suitable for general term formula in fractional form. A term is divided into two or more difference forms, that is, an = f (n+ 1)-f (n), and then many intermediate terms are cancelled when accumulating.