A sequence of numbers `a_0,a_1,a_2,a_3`, ........ satisfies the relation `a_n^2-a_(n-1)a_(n+1)=(-1)^n`. Find `a_3`, given `a_0=1` and `a_1=3`.

A squence of positive terms A_(1),A_(2),A_(3),"....,"A_(n) satisfies the relation A_(n+1)=(3(1+A_(n)))/((3+A_(n))) . Least integeral value of A_(1) for which the sequence is decreasing can be

For the A.P., a_1, a_2,a_3, ............., if a_4/a_7= 2/3 , find a_6/a_8 .

If the sequence a_1, a_2, a_3,....... a_n ,dot forms an A.P., then prove that a_1^2-a_2^2+a_3^2-a_4^2+.......+ a_(2n-1)^2 - a_(2n)^2=n/(2n-1)(a_1^2-a_(2n)^2)

If a_1, a_2, a_3,.....a_n are in H.P. and a_1 a_2+a_2 a_3+a_3 a_4+.......a_(n-1) a_n=ka_1 a_n , then k is equal to

The sequence a_(1),a_(2),a_(3),".......," is a geometric sequence with common ratio r . The sequence b_(1),b_(2),b_(3),".......," is also a geometric sequence. If b_(1)=1,b_(2)=root4(7)-root4(28)+1,a_(1)=root4(28)" and "sum_(n=1)^(oo)(1)/(a_(n))=sum_(n=1)^(oo)(b_(n)) , then the value of (1+r^(2)+r^(4)) is

Let A be the set of 4-digit numbers a_1 a_2 a_3 a_4 where a_1 > a_2 > a_3 > a_4 , then n(A) is equal to

Find the terms indicated in the following case : a_n =(n-1)(2-n) (3+n), a_1, a_2, a_3 .

If a_1,a_2,a_3,……………….. are in A.P., then the value of: {:|(a_1,a_2,1),(a_2,a_3,1),(a_3,a_4,1)| is equal to

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 .

The Fibonacci sequence is defined by 1 = a_1= a_2 and a_n=a_(n-1)+a_(n-2) , n>2 . Find (a_(n+1))/a_n , for n = 1, 2, 3, 4, 5