Question 1: Since a 1 is arithmetic progression, directly change the conditions of a2, S4(=a 1+a2+a3+a4) into the basic quantities a 1 and D, and solve the binary linear equation to get an=3n-2.

The second problem is the divisibility with remainder in analogy primary schools, that is, the quotient of an divided by 4 is bn and the remainder is cn.

Then there are cn = an-4bn = 3n-2-4bn 1, c(n+4)=3n+ 10-b(n+4)②. It can be seen that the correlation of CN can be expressed by an and bn. If we want to find two expressions of cn=c(n+4), that is, ① and ② are equal, we should

Solution of bn: Because an is an increasing sequence, an/4 must also be an increasing sequence, that is, bn is an increasing sequence.

And because bn∈N, that is, bn is an increasing arithmetic series, and its term is a natural number, b 1=0 and d= 1, bn=n- 1.

So cn=3n-2-4(n- 1)=2-n, c (n+4) = 3n+10-4 (n+4-1) = 2-n.

So cn=c(n+4)