[" (3) "(a_(1)=3,a_(n)=3a_(n-1)+2794n>=1(1)/(9n)sqrt(6 pi)],[" (c) "a_(1)=a_(2)=2,a_(n)=a_(n-1)-1sqrt(181)n>2]quad " (b) "a_(1)=-1,a_(n)=(a_(n-1))/(n)," and "n>=2

Find the next five terms of each of the following sequences given by: a_(1)=1,a_(n)=a_(n-1)+2,n>=2a_(1)=a_(2)=2,a_(n)=a_(n-1)-3,n>2a_(1)=-1,a_(n)=(a_(n-1))/(n),n>=2a_(1)=4,a_(n)=4a_(n-1)+3,n>1

If a_(1)=2 and a_(n)-a_(n-1)=2n(n>=2), find the value of a_(1)+a_(2)+a_(3)+....+a_(20)

B={a_(n):n in N,a_(n)+1=2a_(n) and a_(1)=3}

If quad 1,a_(1)=3 and a_(n)^(2)-a_(n-1)*a_(n+1)=(-1)^(n) Find a_(3).

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

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)),f or n=5

If a_(1), a_(2),…a_(n) are in H.P. then a_(1).a_(2) + a_(2).a_(3) + a_(3).a_(4) + …+ a_(n-1) .a_(n) =

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

Let a_(1),a_(2),a_(3), . . .,a_(n) be an A.P. Statement -1 : (1)/(a_(1)a_(n))+(1)/(a_(2)a_(n-1))+(1)/(a_(3)a_(n-1))+ . . .. +(1)/(a_(n)a_(1)) =(2)/(a_(1)+a_(n))((1)/(a_(1))+(1)/(a_(2))+ . . .. +(1)/(a_(n))) Statement -2: a_(r)+a_(n-r+1)=a_(1)+a_(n)" for "1lerlen

If a_(1),a_(2),a_(3),,a_(n) are an A.P.of non-zero terms, prove that _(1)(1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))++(1)/(a_(n-1)a_(n))=(n-1)/(a_(1)a_(n))