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

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

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

Let a_(1), a_(2), a_(3).... and b_(1), b_(2), b_(3)... be arithmetic progression such that a_(1) = 25, b_(1) = 75 and a_(100) + b_(100) = 100 . Then

"If "a_1,a_2,a_3,.....,a_n" are in AP, prove that "a_(1)+a_(n)=a_(r)+a_(n-r+1)""

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)

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

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

Let a_(1), a_(2),…. and b_(1),b_(2),…. be arithemetic progression such that a_(1)=25 , b_(1)=75 and a_(100)+b_(100)=100 , then the sum of first hundred term of the progression a_(1)+b_(1) , a_(2)+b_(2) ,…. is equal to

If a_(1),a_(2),a_(3),a_(4) are in HP, then (1)/(a_(1)a_(4))sum_(r=1)^(3)a_(r)a_(r+1) is root of :

Let b_(i)gt1" for "i=1,2,"......",101 . Suppose log_(e)b_(1),log_(e)b_(2),log_(e)b_(3),"........"log_(e)b_(101) are in Arithmetic Progression (AP) with the common difference log_(e)2 . Suppose a_(1),a_(2),a_(3),"........"a_(101) are in AP. Such that, a_(1)=b_(1) and a_(51)=b_(51) . If t=b_(1)+b_(2)+"........."+b_(51)" and " s=a_(1)+a_(2)+"........."+a_(51) , then