solve : `a_(n)=(-1)^(n)n;a_(3),a_(5),a_(8)`

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) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(1)+a_(2)+a_(3)+a_(4)+a_(5)...+a_(n) for all a_(i)>0,i=1,2,3dots n. Then the maximum value of a_(1)^(2)a_(2)a_(3)a_(4)a_(5)..a_(n) is

If n^(th) terms of the sequence {a_(n)} where a_(n)=(-1)^(n-1)5^(n+1) , find a_(1),a_(2) , and a_(3) is

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))

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

If a_(1),a_(2),...a_(n) are in H.P then the expression a_(1)a_(2)+a_(2)a_(3)+...+a_(n-1)a_(n) is equal to