已知f(x)=(x-1)平方,g(x)=4(x-1),数列an满足a1=2,已知f(x)=(x-1)平方,g(x)=4(x-1),数列an满足a1=2,[a(n+1)-an]g(an)+f(an)=0,数列bn满足bn=3f(an)-g[a(n+1)],求bn的最大项和最小项.说明：题中的（n+1）为底.

Question

已知f(x)=(x-1)平方,g(x)=4(x-1),数列an满足a1=2,
已知f(x)=(x-1)平方,g(x)=4(x-1),数列an满足a1=2,[a(n+1)-an]g(an)+f(an)=0,数列bn满足bn=3f(an)-g[a(n+1)],求bn的最大项和最小项.
说明：题中的（n+1）为底.

Answer 1

[a(n+1)-an]g(an)+f(an)=0,(a(n+1)-an)4(an-1)+(an-1)²=0,an不等于14(a(n+1)-an)+an-1=0,a(n+1)=3/4an+1/4a(n+1)-1=3/4(an-1)an-1=(3/4)^(n-1)(a1-1),an=(3/4)^(n-1)+1bn=3(an-1)²-g(3/4an+1/4)=3(an-1)&s...