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]|`

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 evaluate |[3, 1+s_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 evaluate |[3, 1+s_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 evaluate |[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 alphaa n dbeta are the roots of ax^2+bx+c=0a n dS_n=alpha^n+beta^n, then a S_(n+1)+b S_n+c S_(n-1)=0

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 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