Let `a_(n)` be the nth term of an AP, if `sum_(r=1)^(100)a_(2r)= alpha " and "sum_(r=1)^(100)a_(2r-1)=beta`, then the common difference of the AP is

Let a_n be the n^(t h) term of an A.P. If sum_(r=1)^(100)a_(2r)=alpha&sum_(r=1)^(100)a_(2r-1)=beta, then the common difference of the A.P. is (a) alpha-beta (b) beta-alpha (c) (alpha-beta)/2 (d) None of these

Let a_n be the nth therm of a G.P of positive numbers .Let Sigma_(n=1)^(100) a_(2n)=alpha and Sigma_(n=1)^(100)a_(an-1)=beta then the common ratio is

Let a_n be the nth term of a G.P. of positive numbers. Let sum_(n=1)^(100)a_(2n)=alpha and sum_(n=1)^(100)a_(2n-1)=beta , such that alpha!=beta , then the common ratio is (a) alpha//beta b. beta//alpha c. sqrt(alpha//beta) d. sqrt(beta//alpha)

Let a_n be the nth term of a G.P. of positive numbers. Let sum_(n=1)^(100)a_(2n)=alphaa n dsum_(n=1)^(100)a_(2n-1)=beta , such that alpha!=beta , then the common ratio is alpha//beta b. beta//alpha c. sqrt(alpha//beta) d. sqrt(beta//alpha)

Let sum_(r=1)^(n) r^(6)=f(n)," then "sum_(n=1)^(n) (2r-1)^(6) is equal to

Let a_n be the n^(th) term, of a G.P of postive terms. If Sigma_(n=1)^(100)a_(2n+1)= 200 and Sigma_(n=1)^(100)a_(2n)=100, " then" Sigma_(n=1)^(200)a_(n)

Let a_n is a positive term of a GP and sum_(n=1)^100 a_(2n + 1)= 200, sum_(n=1)^100 a_(2n) = 200 , find sum_(n=1)^200 a_(2n) = ?

a_(1),a_(2),a_(3),a_(4),a_(5), are first five terms of an A.P. such that a_(1) +a_(3) +a_(5) = -12 and a_(1) .a_(2) . a_(3) =8 . Find the first term and the common difference.

If a_(n) be the n^(th) term of an AP and if a_(1) = 2 , then the value of the common difference that would make a_(1) a_(2) a_(3) minimum is _________

If a_(1), a_(2), a_(3) ,... are in AP such that a_(1) + a_(7) + a_(16) = 40 , then the sum of the first 15 terms of this AP is