If `a ,b ,c ,d` are distinct integers in an A.P. such that `d=a^2+b^2+c^2,` then find the value of `a+b+c+ddot`

If a, b, c, d are distinct positive numbers in A.P., then:

If a ,\ b ,\ c are distinct positive prime integers such that a^2b^3c^4=49392 ,\ find the value of a ,\ b\ and c

If a ,b ,c ,d ,e are in A.P., the find the value of a-4b+6c-4d+edot

If the numbers a , b , c , d , e form an A.P. , then find the value of a-4b+6c-4d+edot

If the integers a,b,c,d are in arithmetic progression and a lt b lt c lt d and d=a^(2)+b^(2)+c^(2) , the value of (a+10b+100c+1000d) is

If a, b, c are distinct real numbers such that a, b, c are in A.P. and a^2, b^2, c^2 are in H. P , then

If a,b , c are in AP, then, find the value of (a-c)^2/(b^2-ac)

Let a ,b ,c ,d be four distinct real numbers in A.P. Then half of the smallest positive valueof k satisfying a(a-b)+k(b-c)^2=(c-a)^3=2(a-x)+(b-d)^2+(c-d)^3 is __________.

Let a ,b ,c ,d be four distinct real numbers in A.P. Then the smallest positive valueof k satisfying 2(a-b)+k(b-c)^2+(c-a)^3=2(a-d)+(b-d)^2+(c-d)^3 is __________.

If a ,b ,c ,da n dp are distinct real numbers such that (a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0, then prove that a ,b ,c , d are in G.P.