IF `a_(1),a_(2),a_(3),"...."a_(10)` be in AP and `h_(1),h_(2),h_(3),"...."h_(10)` be in HP. If `a_(1)=h_(1)=2` and `a_(10)=h_(10)=3`, then find value of `a_(4)h_(7)`.

Let a_(1),a_(2),"...." be in AP and q_(1),q_(2),"...." be in GP. If a_(1)=q_(1)=2 " and "a_(10)=q_(10)=3 , then

If a_(1),a_(2),a_(3),".....",a_(n) are in HP, than prove that a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+"....."+a_(n-1)a_(n)=(n-1)a_(1)a_(n)

If a_(1),a_(2)a_(3),….,a_(15) are in A.P and a_(1)+a_(8)+a_(15)=15 , then a_(2)+a_(3)+a_(8)+a_(13)+a_(14) is equal to

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_(1), a_(2), a_(3).... A_(n) in R^(+) and a_(1).a_(2).a_(3).... A_(n) = 1 , then minimum value of (1 + a_(1) + a_(1)^(2)) (a + a_(2) + a_(2)^(2)) (1 + a_(3) + a_(3)^(2))..... (1 + a_(n) + a_(n)^(2)) is equal to

For an increasing G.P. a_(1), a_(2), a_(3),.....a_(n), " If " a_(6) = 4a_(4), a_(9) - a_(7) = 192 , then the value of sum_(l=1)^(oo) (1)/(a_(i)) is

If a_(1),a_(2),a_(3),"........" is an arithmetic progression with common difference 1 and a_(1)+a_(2)+a_(3)+"..."+a_(98)=137 , then find the value of a_(2)+a_(4)+a_(6)+"..."+a_(98) .

If a and b are distinct positive real numbers such that a, a_(1), a_(2), a_(3), a_(4), a_(5), b are in A.P. , a, b_(1), b_(2), b_(3), b_(4), b_(5), b are in G.P. and a, c_(1), c_(2), c_(3), c_(4), c_(5), b are in H.P., then the roots of a_(3)x^(2)+b_(3)x+c_(3)=0 are

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

Let a_(1),a_(2),a_(3),a_(4)anda_(5) be such that a_(1),a_(2)anda_(3) are in A.P., a_(2),a_(3)anda_(4) are in G.P., and a_(3),a_(4)anda_(5) are in H.P. Then, a_(1),a_(3)anda_(5) are in