If `alphaa n dbeta` are the roots of `x^2-p(x+1)-c=0a n dS_n=alpha^n+beta,` then `a S_(n+1)+b S_n+c S_(n-1)=0` and hence find `S_5dot`

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 and hence find S_5dot

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, beta be the real roots of ax^2+bx+c=0 , and s_n=alpha^n + beta^n then prove that as_n + bs_(n-1)+cs_(n-2)=0 .for all n in N .

If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta)+(beta)/(alpha)) then N=

If alphaa n dbeta are the rootsof he equations x^2-a x+b=0a n dA_n=alpha^n+beta^n , then which of the following is true? a. A_(n+1)=a A_n+b A_(n-1) b. A_(n+1)=b A_(n-1)+a A_n c. A_(n+1)=a A_n-b A_(n-1) d. A_(n+1)=b A_(n-1)-a A_n

Let alpha and beta be the roots of the equation x^(2) -px+q =0 and V_(n) = alpha^(n) + beta^(n) , Show that V_(n+1) = pV_(n) -qV_(n-1) find V_(5)

If alpha,beta are the roots of the equation x^2-2x+4=0 , find alpha^(n)+beta^(n) for (a) n=3k, k in N

Let alpha and beta be the roots of the equation 5x^2+6x-2=0 . If S_n=alpha^n+beta^n, n=1,2,3.... then

If alpha,beta are the roots of equation x^(2)-10x+2=0 and a_(n)=alpha^(n)-beta^(n) then sum_(n=1)^(50)n.((a_(n+1)+2a_(n-1))/(a_(n))) is more than (a)12500 (b)12250 (c)12750 (d)12000

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]|