[a_(n)=(n^(2))/(2^(n));a_(7)],[a_(n)=(n(n-2))/(n+3);a_(20)]

Find the term indicated in each case: (i) a_(n)=(n^(2))/(2^(n)):a_(7) (ii) a_(n)=(n(n-2))/(n-3),a_(20) (iii) a_(n)=[(1+(-1)^(n))/2 3^(n)],a_(7)

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)

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 the sequence a_(1),a_(2),a_(3),...,a_(n) from an A.P.Then the value of a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-...+a_(2n-1)^(2)-a_(2n)^(2) is (2n)/(n-1)(a_(2n)^(2)-a_(1)^(2))(b)(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))(n)/(n+1)(a_(1)^(2)-a_(2n)^(2))(d)(n)/(n-1)(a_(1)^(2)+a_(2n)^(2))

If a_(n) = (n^(2))/(2^(n)) , then find a_(7) .

If a_(1),a_(2),a_(3),...,a_(2n+1) are in A.P.then (a_(2n+1)-a_(1))/(a_(2n+1)+a_(1))+(a_(2n)-a_(2))/(a_(2n)+a_(2))+...+(a_(n+2)-a_(n))/(a_(n+2)+a_(n)) is equal to (n(n+1))/(2)xx(a_(2)-a_(1))/(a_(n+1)) b.(n(n+1))/(2) c.(n+1)(a_(2)-a_(1)) d.none of these

If a_(1), a_(2),a_(3), cdots , a_(2n+1) are in A.P then (a_(2n+1)-a_(1))/(a_(2n+1)+a_(1)) + (a_(2n)-a_(2))/(a_(2n)+a_(2))+cdots+ (a_(n+_2)-a_(n))/(a_(n+2)+a_(n)) is equal to

If a_(1),a_(2),...,a_(n)>0, then prove that (a_(1))/(a_(2))+(a_(2))/(a_(3))+(a_(3))/(a_(4))+...+(a_(n-1))/(a_(n))+(a_(n))/(a_(1))>n

If a_(1),a_(2)...a_(n) are the first n terms of an Ap with a_(1)=0 and d!=0 then (a_(3)-a_(2))/(a_(2))+(a_(4)-a_(2))/(a_(3))+(a_(5)-a_(2))/(a_(4))...+(a_(n)-a_(2))/(a_(n-1)) is