Find `a_(1), a_(2), a_(3)` : `a_(n)=a_(n-1)+(1)/(2),a_(1)=-1`

If a_(1),a_(2),a_(3)….a_(n) are positive and (n-1)s = a_(1)+a_(2)+….+ a_(n) then prove that a_(1),a_(2),a_(3)…a_(n) ge (n-1)^(n)(s-a_(1))(s-a_(2))….(s-a_(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)),f or n=5

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

Find the indicated terms in each of the following sequences whose nth terms are: a_(n)=5_(n)-4;a_(12) and a_(15)a_(n)=(3n-2)/(4n+5);a+7 and a_(8)a_(n)=n(n-1);a_(5)anda_(8)a_(n)=(n-1)(2-n)3+n);a_(1),a_(2),a_(3)a_(n)=(-1)^(n)n;a_(3),a_(5),a_(8)

If a_(1), a_(2), a_(3).... A_(n) in R^(+) and a_(1).a_(2).a_(3).... A_(n) = 1 , then minimum value of (1 + a_(1) + a_(1)^(2)) (a + a_(2) + a_(2)^(2)) (1 + a_(3) + a_(3)^(2))..... (1 + a_(n) + a_(n)^(2)) is equal to

a1,a2,a3.....an are in H.P. (a_(1))/(a_(2)+a_(3)+ . . .+a_(n)),(a_(2))/(a_(1)+a_(3)+ . . . +a_(n)),(a_(3))/(a_(1)+a_(2)+a_(4)+ . . .+a_(n)), . . .,(a_(n))/(a_(1)+a_(2)+ . . . +a_(n-1)) are in

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

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