If `a_n,a_(n+1),a_(n+2)` are three consecutive terms of an AP, then `2a_(n+1)=a_n+a_(n+2)`

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

If a_(1),a_(2),a_(3),......,a_(n) are consecutive terms of an increasing A.P.and (1^(2)-a_(1))+(2^(2)a_(2))+(3^(2)a_(3))+.........+(n^(2)-a_(n))=((n-1)*n*(n+1))/(3) then the value of ((a_(5)+a_(3)-a_(2))/(6)) is equal to

If a_(1),a_(2),...,a_(n) be an A.P. of positive terms, then

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))

Let a_(1),a_(2),...,a_(n) .be sequence of real numbers with a_(n+1)=a_(n)+sqrt(1+a_(n)^(2)) and a_(0)=0 Prove that lim_(n rarr oo)((a_(n))/(2^(n-1)))=(2)/(pi)

. If a_(1),a_(2),a_(3),...,a_(2n+1) are in AP then (a_(2n+1)+a_(1))+(a_(2n)+a_(2))+...+(a_(n+2)+a_(n)) is equal to

If a_(m) be the mth term of an AP, show that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+"...."+a_(2n-1)^(2)-a_(2n)^(2)=(n)/((2n-1))(a_(1)^(2)-a_(2n)^(2)) .