If a, b, c and d are in G.P. show that `(a^2+b^2+c^2)(b^2+c^2+d^2) = (ab+bc+cd)^2`

If a, b, c are in HP show that ab + bc = 2ac.

If a, b, c, d and p are different real numbers such that (a^2 + b^2 + c^2)p^2 – 2(ab + bc + cd) p + (b^2 + c^2 + d^2) le 0 , then show that a, b, c and d are in GP.

If a,b, and c are in G.P then a+b,2b and b+ c are in

If a, b, c, d are in G.P., then (a + b + c + d)^(2) is equal to

If a , b, c, … are in G.P. then 2a,2b,2c,… are in ….

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.

If a ,b ,a n dc are in H.P., then th value of ((a c+a b-b c)(a b+b c-a c))/((a b c)^2) is ((a+c)(3a-c))/(4a^2c^2) b. 2/(b c)-1/(b^2) c. 2/(b c)-1/(a^2) d. ((a-c)(3a+c))/(4a^2c^2)

If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

If a, b, d and p are distinct non - zero real numbers such that (a^2+b^2 + c^2) p^2 - 2(ab+bc+cd)p+(b^2 + c^2 +d^2) le 0 then n. Prove that a, b, c, d are in G. P and ad = bc

If a,b,c,d are in a geometric sequences, then show that (a-b+c) (b+c+d) = ab + bc + cd.