Let `(a_(1),b_(1))` and `(a_(2),b_(2))` are the pair of real numbers such that 10,a,b,ab constitute an arithmetic progression. Then, the value of `((2a_(1)a_(2)+b_(1)b_(2))/(10))` is

If the ordered pairs of natural numbers (a_(1), b_(1)) and (a_(2), b_(2)) are satisfying the equation are cot^(-1)8=tan^(-1)a-tan^(-1)b . Then the value of (a_(1)+b_(1)+a_(2)+b_(2))/9 is

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

If a_(1),a_(2),...,.,a_(10) are positive numbers in arithmetic progression such that (1)/(a_(1)a_(2))+(1)/(a_(2)a_(3))+...*+(1)/(a_(9)a_(10))=(9)/(64) and (1)/(a_(1)a_(10))+(1)/(a_(2)a_(9))+......(1)/(a_(10)a_(1))=(1)/(10)((1)/(a_(1))+...+(1)/(a_(10))) then the value of (2)/(5)((a_(1))/(a_(10))+(a_(10))/(a_(1))) is

Let a_(1), a_(2), a_(3)... be a sequance of positive integers in arithmetic progression with common difference 2. Also let b_(1),b_(2), b_(3)...... be a sequences of posotive intergers in geometric progression with commo ratio 2. If a_(1)=b_(1)=c_(2) . then the number of all possible values of c, for which the equality. 2(a_(1)+a_(2).+.....+a_(n))=b_(1)+b_(2)+....+b_(n) holes for same positive integer n, is

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

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

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

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_(51) are arithmetic means inserted between the number a and b, then find the value of ((b + A_(51))/(b - A_(51))) - ((A_(1) + a)/(A_(1) - a))