It is known that {an} and {BN} are arithmetic sequences with non-zero tolerance, then the sequence {an + BN}, {BN an}, {3an BN}, {5An + 4} How many of {anbn}, {an & sup2;} are arithmetic sequences? Ans: 4 Please help me~

It is known that {an} and {BN} are arithmetic sequences with non-zero tolerance, then the sequence {an + BN}, {BN an}, {3an BN}, {5An + 4} How many of {anbn}, {an & sup2;} are arithmetic sequences? Ans: 4 Please help me~

According to the definition of arithmetic sequence, that is, the value of the latter minus the former is constant (tolerance)
For example:
For the sequence {an + BN}
[a（n+1）+b（n+1）]-(an+bn)=a（n+1）-an+b（n+1）-bn
That is, the sum of the tolerances of the two sequences is a constant
So the sequence is an arithmetic sequence
In the same way, we can deduce that the first four are arithmetic sequences, while the last two are not