The second-order arithmetic progression, called the difference arithmetic progression, is the last term of the series minus the first term, and the new series is arithmetic progression.

For example, 3, 7, 12, 18, and 25 are all secondary arithmetic progression.

7-3=4, 12-7=5,18-12 = 6,25-18 = 7 secondary arithmetic progression; Using the difference formula, the general term formula of the second-order arithmetic progression can be given:

an = a 1+(a2-a 1)(n- 1)+(a3-2 a2+a 1)(n- 1)(n-2)/2；

Where a1-2a2+a3 = (a3-a2)-(a2-a1) can also be called the tolerance of quadratic arithmetic progression.

Extended data:

Sequence not only has a wide range of practical applications, but also plays a role in connecting the past with the future.

On the one hand, sequence, as a special function, is inseparable from function thought; On the other hand, learning sequence is also a preparation for further learning the limit of sequence. On the other hand, on the basis of students' learning the concept of sequence, arithmetic progression gave two methods of sequence-general formula and recursive formula, which further deepened and broadened his understanding of sequence.

The general formula is: an = a1+(n-1) * D. The first term a 1= 1, and the tolerance d=2. The first n terms and formulas are: sn = a1* n+[n * (n-1) * d]/2 or Sn=[n*(a 1+an)]/2. Note: All the above n are positive integers.