" 1."a_(n)=(3n+1)/(5)

If (1+x+x^(2))^(n)=1 +a_(1)x+a_(2)x^(2)+a_(3)x^(3) +……..+a_(2n).x^(2n) then prove that: (i) a_(1)+a_(3)+a_(5)+…..+a_(2n-1) =(3^(n)-1)/(2) (ii) a_(2)+a_(4)+a_(6)+……+a_(2n)=(3^(n)-1)/(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

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

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_(n)=(1)/(n+1)+1 then find the vaue of a_(1)+a_(3)+a_(5)

If a_(n)=(n^(2))/(3n+2) , find a_(1)a_(5) .

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

Let a sequence {a_(n)} be defined by a_(n)=(1)/(n+1)+(1)/(n+2)+(1)/(n+3)+"....."(1)/(3n) , then