The function y = f (x) defined on positive integer set has f (a + b) = f (a) * f (b) constant for any a, B ∈ n Let f (1) = a ≠ 0, if an = f (n) (n ∈ n +) (1) Prove: the sequence {an} is an equal ratio sequence, and find out the general term formula of the sequence {an} (2) If Sn = a1 + A2 + +An, the sequence {sn-2an} is an equal ratio sequence, find the value of real number a

The function y = f (x) defined on positive integer set has f (a + b) = f (a) * f (b) constant for any a, B ∈ n Let f (1) = a ≠ 0, if an = f (n) (n ∈ n +) (1) Prove: the sequence {an} is an equal ratio sequence, and find out the general term formula of the sequence {an} (2) If Sn = a1 + A2 + +An, the sequence {sn-2an} is an equal ratio sequence, find the value of real number a

1: An + 1 = f (n + 1) = f (n) * f (1) = AF (n) because a is not equal to 0 and A1 = a is not equal to 0
An + 1 / an = a, so an is an equal ratio sequence
an=a1*a^(n-1)=a^n
2:Sn-2an
1: When a = 1, Sn = Na1 = Na
Sn-2an=na-2a=(n-2)a=n-2
A2 = 0, so it is not an equal ratio sequence, so a is not equal to 1
2：Sn=a(1-a^n)/(1-a)
Sn-2an= a(1-a^n)/(1-a)- 2a^n=(a-a^(n+1)-2a^n+2a^(n+1))/(1-a)
=(a-2a^n+a^(n+1))/(1-a) =(a-a^n（2-a）)/(1-a)
Let the common ratio of {sn-2an} be K as the fixed value
Sn+1-2an+1/(Sn-2an) = (a-2a^（n+1）+a^(n+2))/(a-2a^n+a^(n+1)) = k
a-2a^（n+1）+a^(n+2) = ka -2a^n k +a^(n+1) k
a-ka=a^(n+1)[2-a-2k/a+k]
1-k=a^(n)[2-a-2k/a +k]
The formula is independent of N, so both sides are 0
1-k=0
2-a-2k/a +k=0-->k=0 a=2