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 `alpha-beta` (b) `beta-alpha` `(alpha-beta)/2` (d) None of these

Let a_(n) be the n^(th) 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 alpha-beta(b)beta-alpha(alpha-beta)/(2)quad (d) None of these

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 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 alpha/ beta b.beta/ alpha c.sqrt(alpha/ beta) d.sqrt(beta/ alpha)

If sum_(r=1)^9 ((r+3)/2^r)(.^9C_r)=alpha(3/2)^9+beta , then alpha+beta is equal to :

Sum of n terms of the series sinalpha-sin(alpha+beta)+sin(alpha+2beta)-sin(alpha+3beta)+….

If alpha_(1), alpha_(2), alpha_(3), beta_(1), beta_(2), beta_(3) are the values of n for which sum_(r=0)^(n-1)x^(2r) is divisible by sum_(r=0)^(n-1)x^(r ) , then the triangle having vertices (alpha_(1), beta_(1)),(alpha_(2),beta_(2)) and (alpha_(3), beta_(3)) cannot be

If sum_(r=0)^(n){a_(r)(x-alpha+2)^(r)-b_(r)(alpha-x-1)^(r)}=0 then prove that b_(n)-(-1)^(n)a_(n)=0