Given that `a_(4)+a_(8)+a_(12)+a_(16)=224`, the sum of the first nineteen terms of the arithmetic progression
`a_(1),a_(2),a_(3),….` is equal to

If a_(1)+a_(5)+a_(10)+a_(15)+a_(24)=225 , then the sum of the first 24 terms of the arithmetic progression a_(1), a_(2), a_(3)…….. is equal to

If a_(1)+a_(5)+a_(10)+a_(15)+a_(20)=225 , then the sum of the first 24 terms of the arithmetic progression a_(1), a_(2), a_(3)…….. is equal to

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), cdots and b_(1), b_(2) cdots be arithmetic progression 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), cdots is

If a_(1),a_(2),a_(3),..., are in arithmetic progression,then S=a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+...-a_(2k)^(2) is equal

If a_(1), a_(2), a_(3) ,…., a_(n) are the terms of arithmatic progression then prove that (1)/(a_(1)a_(2)) + (1)/(a_(2)a_(3)) + (1)/(a_(3)a_(4)) + ….+ (1)/(a_(n-1) a_(n)) = (n-1)/(a_(1)a_(n))

If a_(1), a_(2), a_(3), a_(4), a_(5) are consecutive terms of an arithmetic progression with common difference 3, then the value of |(a_(3)^(2),a_(2),a_(1)),(a_(4)^(2),a_(3),a_(2)),(a_(5)^(2),a_(4),a_(3))| is

If a_(1), a_(2), a_(3), a_(4), a_(5) are consecutive terms of an arithmetic progression with common difference 3, then the value of |(a_(3)^(2),a_(2),a_(1)),(a_(4)^(2),a_(3),a_(2)),(a_(5)^(2),a_(4),a_(3))| is