If a, b, c are in GP, prove that `1/((a+b)), 1/(2b), 1/(b+c)` are in AP.

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If a, b, c are in G.P., prove that 1/(a + b), 1/(2b), 1/(b + c) are in A.P. If a, b, c are in G.P., prove that 1/(a + b), 1/(2b), 1/(b + c) are in A.P.
If a,b,c are in A.P., b,c,d are in G.P. and 1/c , 1/d , 1/e are in A.P., prove that a,c,e are in G.P If a,b,c are in A.P., b,c,d are in G.P. and 1/c , 1/d , 1/e are in A.P., prove that a,c,e are in G.P
If a, b, c are in GP, prove that 1/(a+b), 1/2 b, 1/b+c are in AP. If a, b, c are in GP, prove that 1/(a+b), 1/2 b, 1/b+c are in AP.
If a, b and c are in the G.P such that a^(1/x) = b^(1/y) = c^(1/z), prove that: x+z=2y. If a, b and c are in the G.P such that a^(1/x) = b^(1/y) = c^(1/z), prove that: x+z=2y.
if a,b,c are in A P; b,c,d are in G P and 1/c,1/d,1/e are in A.P . prove that a,c,e are in G.P if a,b,c are in A P; b,c,d are in G P and 1/c,1/d,1/e are in A.P . prove that a,c,e are in G.P
If (1)/(a+b),(1)/(2b),(1)/(b+c) are in A.P., then prove that a, b, c are in G.P. | 11 | SEQUENCE... If (1)/(a+b),(1)/(2b),(1)/(b+c) are in A.P., then prove that a, b, c are in G.P. | 11 | SEQUENCE...
If `a ,b ,c` are in G.P., prove that: 1) `a(b^2+c^2)=c(a^2+b^2)` , 2) `A^2b^2c^2(1/(a^3)+1/(b^3)... If `a ,b ,c` are in G.P., prove that: 1) `a(b^2+c^2)=c(a^2+b^2)` , 2) `A^2b^2c^2(1/(a^3)+1/(b^3)...
If `a ,b ,c` are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)` If `a ,b ,c` are in G.P. then prove that `(a^2+a b+b^2)/(b c+c a+a b)=(b+a)/(c+b)`