Justify whether it is true to say that ` -1, (-3)/(2), -2, (5)/(2), … ` Forms an AP as `a_(2)-a_(1)=a_(3)-a_(2)`.

If the sequence a_(1),a_(2),a_(3),dots a_(n),.... forms an A.P.then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)+...+a_(4)^(2)=(n)/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If a_(1),a_(2),a_(3),a_(4),,……, a_(n-1),a_(n) " are distinct non-zero real numbers such that " (a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + …..+ a_(n-1)^(2))x^2 + 2 (a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) + ……+ a_(n-1) a_(n))x + (a_(2)^(2) +a_(3)^(2) + a_(4)^(2) +......+ a_(n)^(2)) le 0 " then " a_(1), a_(2), a_(3) ,....., a_(n-1), a_(n) are in

It a_(1) , a_(2) , a_(3) a_(4) be in G.P. then prove that (a_(2)-a_(3))^(2) + (a_(3) - a_(1))^(2) + (a_(4) +a_(2))^(2) = (a_(1)-a_(4))^(2)

Find the sum of first 24 terms of the A.P. a_(1) , a_(2), a_(3) ...., if it is know that a_(1) + a_(5) + a_(10) + a_(15) + a_(20) + a_(24) = 225

If the sequence a_(1),a_(2),a_(3),…,a_(n) is an A.P., then prove that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+…+a_(2n-1)^(2)-a_(2n)^(2)=n/(2n-1)(a_(1)^(2)-a_(2n)^(2))

If a_(1),a_(2)...a_(n) are the first n terms of an Ap with a_(1)=0 and d!=0 then (a_(3)-a_(2))/(a_(2))+(a_(4)-a_(2))/(a_(3))+(a_(5)-a_(2))/(a_(4))...+(a_(n)-a_(2))/(a_(n-1)) is

If a_(m) be the mth term of an AP, show that a_(1)^(2)-a_(2)^(2)+a_(3)^(2)-a_(4)^(2)+"...."+a_(2n-1)^(2)-a_(2n)^(2)=(n)/((2n-1))(a_(1)^(2)-a_(2n)^(2)) .

Suppose a_(1),a_(2)… are in A.P. If a_(8): a_(5)= 3:2, then a_(17) : a_(23) is :

Let A and B be two sets such that n(A) = 5 and n(B) = 2 . If (a_(1), 2), (a_(2), 3), (a_(3), 2), (a_(4), 3), (a_(5), 2) are in A xx B and a_(1), a_(2), a_(3), a_(4) and a_(5) are distinct, find A and B.