设数列{An}的前n项和为Sn,已知A1=1,A2=6,A3=11,且(5n-8...

2025-05-20 03:15:12
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回答(1):

(5n-8)S(n+1)—(5n+2)Sn=Pn+B(5n-8)a(n+1)-10Sn=Pn+B
(1)
S(n+1)—Sn=a(n+1)(5n-3)a(n+2)-10S(n+1)==P(n+1)+B
(2)
让n变成n+1(2)-(1)(5n-3)a(n+2)-(5n+2)a(n+1)=P
(3)(5n+2)a(n+3)-(5n+7)a(n+2)=P
(4)
让n变成n+1(4)-(3)(5n+2)a(n+3)+(5n+2)a(n+1)-(10n+4)a(n+2)=0a(n+3)+a(n+1)=2a(n+2)所以得到它是等差数列