s(n- 1)= 2A(n- 1)-3(n- 1)

An = Sn -S(n- 1)= 2 An -2A(n- 1)+3.

An +3 = 2A(n- 1)

Namely: (An-3) = 2[A(n- 1)-3]

An -3 constitutes a geometric series, and An -3 = (a 1-3) * 2 (n- 1).

An = 3+(a1-3) * 2 (n-1)

If there is an arithmetic subcolumn, set it to k.

Then you need 2 (k-1)+2 (n-1) = 2 (m-1) * 2.

2 (k- 1).

1+2^(n-k) = 2^(m-k+ 1)

This formula is only possible when n=k or m-k+ 1=0 (otherwise, even number subtraction cannot be equal to 1).

Because m, n, k n and k are not equal to each other, it seems that it is only possible when k=m+ 1, and at this time the right side of the equation is 1 and the left side is 1 plus a positive number, which is impossible.

Therefore, there is no such arithmetic subsequence.