let `f(x)` be a polynomial function of second degree. If `f(1)=f(-1)and a_(1),a_(2),a_(3)` are in AP, then show that `f'(a_(1)),f'(a_(2)),f'(a_(3))` are in AP.

If a_(1),a_(2),a_(3),…. are in A.P., then a_(p),a_(q),a_(r) are in A.P. if p,q,r are in

If a_(n)=3-4n , then show that a_(1),a_(2),a_(3), … form an AP. Also, find S_(20) .

If a_(1),a_(2),a_(3),a_(4),a_(5) are in HP, then a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+a_(4)a_(5) is equal to

If the coefficients of 4 consecutive terms in the expansion of (1+x)^(n) are a_(1),a_(2),a_(3),a_(4) respectively, then show that (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

Suppose a_(1), a_(2) , .... Are real numbers, with a_(1) ne 0 . If a_(1), a_(2), a_(3) , ... Are in A.P., then

Let n in N . If (1+x)^(n)=a_(0)+a_(1)x+a_(2)x^(2)+…….+a_(n)x^(n) and a_(n)-3,a_(n-2), a_(n-1) are in AP, then :

If a_(i)gt0 for i u=1, 2, 3, … ,n and a_(1)a_(2)…a_(n)=1, then the minimum value of (1+a_(1))(1+a_(2))…(1+a_(n)) , is

The number of increasing function from f : AtoB where A in {a_(1),a_(2),a_(3),a_(4),a_(5),a_(6)} , B in {1,2,3,….,9} such that a_(i+1) gt a_(i) AA I in N and a_(i) ne i is

If log_(e )((1+x)/(1-x))=a_(0)+a_(1)x+a_(2)x^(2)+…oo then a_(1), a_(3), a_(5) are in

If a_(a), a _(2), a _(3),…., a_(n) are in H.P. and f (k)=sum _(r =1) ^(n) a_(r)-a_(k) then (a_(1))/(f(1)), (a_(2))/(f (2)), (a_(3))/(f (n)) are in :