It is known that the sum of the first n terms of the sequence (an) is Sn, satisfying an + Sn = 2n. It is proved that the sequence (An-2) is an equal ratio sequence and an is obtained

It is known that the sum of the first n terms of the sequence (an) is Sn, satisfying an + Sn = 2n. It is proved that the sequence (An-2) is an equal ratio sequence and an is obtained

an+Sn=2n
Let n = 1
a1+S1=2=>a1=1
And a (n-1) + s (n-1) = 2 (n-1)
Make a difference with the above formula
an-a(n-1)+an=2
2an-a(n-1)=2
an-2=(1/2)[a(n-1)-2]
Get proof
An-2 first item A1-2 = - 1
Common ratio 1 / 2
an=-1/2^(n-1)