[" Consider A.P "a_(1),a_(2),...a_(n),..." and "G.Pb_(1),b_(2),....b_(n),...],[" such that "a_(1)=b_(1)=1,a_(9)=b_(9)" and "sum_(r=1)^(9)a_(r)=369]

Consider an A.P.a_(1),a_(2),...a_(n),... and the G.P.b_(1),b_(2),...,b_(n),... such that a_(1)=b_(1)=1,a_(9)=b_(9) and sum_(r=1)^(9)a_(r)=369 then b_(6)=27 (b) b_(7)=27b_(8)=81 (d) b_(9)=81

Consider an A.P. a_(1), a_(2), "……"a_(n), "……." and the G.P. b_(1),b_(2)"…..", b_(n),"….." such that a_(1) = b_(1)= 1, a_(9) = b_(9) and sum_(r=1)^(9) a_(r) = 369 , then

If a_(1),a_(2),a_(3)...b_(1),b_(1),b_(2),b_(3)...... are in AP. Such that a_(1)+b_(1)=a_(100)+b_(100)=16 and sum_(x=1)^(n)r(a_(r)+b_(r))=576 the find n

Let a_(1),a_(2),a_(3)... and b_(1),b_(2),b_(3)... be arithmetic progressions such that a_(1)=25,b_(1)=75 and a_(100)+b_(100)=100 then the sum of first hundred terms of the progression a_(1)+b_(1)a_(2)+b_(2) is

Suppose four distinct positive numbers a_(1),a_(2),a_(3),a_(4) are in G.P.Let b_(1)=a_(1),b_(2)=b_(1)+a_(2)*b_(3)=b_(2)+a_(3) and b_(4)=b_(3)+a_(1)

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let Delta=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then prove that

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let Delta=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then prove that

Suppose a_(1),a_(2),a_(3) are in A.P. and b_(1),b_(2),b_(3) are in H.P. and let /_\=|(a_(1)-b_(1),a_(1)-b_(2),a_(1)-b_(3)),(a_(2)-b_(1),a_(2)-b_(2),a_(2)-b_(3)),(a_(3)-b_(1),a_(3)-b_(2),a_(3)-b_(3))| then

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

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