a 1+a2+a3+…+an = n * a 1+n *(n– 1)* d/2 .

Recursive equation in grade five is generally a basic concept in mathematics and has many characteristics. For example, it has a clear structure and its laws can be easily transferred from one equation to other. It also has many recursive properties, and each equation has the same first term, tolerance and number of terms. We can quickly calculate recursive equations according to these three characteristics.

First, we should judge the first n terms and tolerance of the equation. We can use arithmetic progression's arithmetic sequence summation formula to calculate the sum of the first n terms, and the tolerance can be obtained by the difference between two adjacent terms.

Then, we can use arithmetic progression's summation formula to find the sum of the n terms of the equation, that is, a 1+A2+A3+…+An = n * a1+n * (n–1) * d/2, where d is the tolerance and a/kloc-0.

Finally, the sum of the n terms of the equation is calculated, and we can know that the an term of the equation is equal to a1+(n-1) × d. With the an term, we can calculate the number of terms of the equation, that is, the average value of the first n terms of the equation.

Through the above steps, the simple calculation of recursive equation can be realized. The calculation of the first n terms and tolerance is relatively simple, and the algorithm of n terms is also relatively simple, which helps us to calculate each term of the equation quickly and accurately, thus achieving the purpose of simple calculation.