If `a_(1)=1, a_(2)=5 and a_(n+2)=5a_(n+1)-6a_(n), n ge 1`, show by using mathematical induction that `a_(n)=3^(n)-2^(n)`

If a_(1)=5 and a_(n)=1+sqrt(a_(n-1)), find a_(3) .

If a_(1)=3 and a_(n)=2a_(n-1)+5 , find a_(4) .

If a_(1)=1, a_(2)=1, and a_(n)=a_(n-1)+a_(n-2) for n ge 3, find the first 7 terms of the sequence.

Let a_(0)=2,a_1=5 and for n ge 2, a_n=5a_(n-1)-6a_(n-2) . Then prove by induction that a_(n)=2^(n)+3^(n) forall n in Z^+ .

If a_(1)=1,a_(n+1)=(1)/(n+1)a_(n),a ge1 , then prove by induction that a_(n+1)=(1)/((n+1)!)n in N .

If a_(0) = 0.4 and a_(n+1) = 2|a_(n)|-1 , then a_(5) =

If a_(1)=3 and a_(n)=n+a_(n-1) , the sum of the first five term is

If a_(1),a_(2),a_(3),a_(4),,……, a_(n-1),a_(n) " are distinct non-zero real numbers such that " (a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + …..+ a_(n-1)^(2))x^2 + 2 (a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) + ……+ a_(n-1) a_(n))x + (a_(2)^(2) +a_(3)^(2) + a_(4)^(2) +......+ a_(n)^(2)) le 0 " then " a_(1), a_(2), a_(3) ,....., a_(n-1), a_(n) are in

If a_(1)=1 and a_(n)+1=(4+3a_(n))/(3+2a_(n)),nge1"and if" lim_(ntooo) a_(n)=a,"then find the value of a."

Fibonacci sequence is defined as follows : a_(1)=a_(2)=1 and a_(n)=a_(n-2)+a_(n-1) , where n gt 2 . Find third, fourth and fifth terms.