It is known that SN is the sum of the first n terms of the sequence an, and Sn = 2-2an 1. Prove that the sequence an is an equal ratio sequence 2. Find the general term formula of the sequence an 3. Find the first n terms and wn of the sequence {ANSN} We need a specific process

It is known that SN is the sum of the first n terms of the sequence an, and Sn = 2-2an 1. Prove that the sequence an is an equal ratio sequence 2. Find the general term formula of the sequence an 3. Find the first n terms and wn of the sequence {ANSN} We need a specific process

An = SN-S (n-1) = - 2An + 2A (n-1) 3an = 2A (n-1) an / a (n-1) = 2 / 3 equal ratio sequence, common ratio = 2 / 3s1 = 2-2a1 = A1, A1 = 2 / 3an = A1 * q ^ (n-1) = (2 / 3) ^ nansn = (2 / 3) ^ n * (2-2 * (2 / 3) ^ n) = 2 (2 / 3) ^ n-2 (2 / 3) ^ (2n) = (4 / 3) (2 / 3) ^ (n-1) - (8 / 9) (4 / 9) ^ (n-1) wn = [(4 / 3) ((2 / 3) ^ (2 / 3) ^ (2 / 3) ^ (2) ^ (2 / 3) ^ (2) ^ (2 / 3) ^ (2) ^ (2 / 3) ^ (2) ^ (2 / 3) ^ (2) ^