If `alpha,beta` are the roots of `x^(2)+x+1=0`, and `s_(n)=alpha^(n)+beta^(n)`, then `|[3,1+S_(1),1+S_(2)],[1+S_(1),1+S_(2),1+S_(3)],[1+S_(2),1+S_(3),1+S_(4)]|=?`

If alpha,beta are the roots of the equation ax^(2)+bx+c=0 and S_(n)=alpha^(n)+beta^(n), then a S_(n+1)+cS_(n)-1)=

If alpha,beta are the roots of the equation, x^(2)-x-1=0 and S_(n)=2023 alpha^(n)+2024 beta^(n) ,then 2S_(12)=S_(11)+S_(10)

[ Let alpha,beta be the roots of x^(2)-2x+5=0 and let S_(n)=alpha^(n)+beta^(n) for ngt=1, then the value of |[3,1+S_(2),1+S_(3)1+S_(2),1+S_(4),1+S_(5)1+S_(3),1+S_(5),1+S_(6)]| is equal to [ (1) -12544, (2) 12544 (3) -4704, (4) -4712]]

If alpha, beta are roots of 375x^(2)-25x-2=0 and s_(n)=alpha^(n)+beta^(n) , then lim_(n to oo) sum_(r=1)^(n)S_(r) is

alpha and beta are the roots of x^2-x-1=0 and S_n=2023 alpha^n 2024 beta^n then

If alpha , beta are the roots of the equation ax^(2)+bx+c=0 and S_(n)=alpha^(n)+beta^(n) , then aS_(n+1)+bS_(n)+cS_(n-1)=(n ge 2)

If alpha and beta are the roots of the equation ax^(2)+bx+b=0 and S_(n)=alpha^(n)+beta^(n), then aS_(n+1)+bS_(n)+cS_(n-1)=

If alpha and beta are the roots of ax^(2)+bx+c=0andS_(n)=alpha^(n)+beta^(n), then aS_(n+1)+bS_(n)+cS_(n-1)=0 and hence find S_(5)