If a,b,c are in G.P, if and only if b power 2 =
Answers
A term in an arithmetic progression is the arithmetic mean of its two neighboring terms — so in particular, b is the arithmetic mean of x and y. Note that the equation to be proved is equivalent to the statement “b is the harmonic mean of x and y.” Then by the this can only be true if b=x=y .
A term in an arithmetic progression is the arithmetic mean of its two neighboring terms — so in particular, b is the arithmetic mean of x and y. Note that the equation to be proved is equivalent to the statement “b is the harmonic mean of x and y.” Then by the this can only be true if b=x=y .Since a term in a geometric progression is the geometric mean of its two neighbors, b=ac−−√ . Additionally,
A term in an arithmetic progression is the arithmetic mean of its two neighboring terms — so in particular, b is the arithmetic mean of x and y. Note that the equation to be proved is equivalent to the statement “b is the harmonic mean of x and y.” Then by the this can only be true if b=x=y .Since a term in a geometric progression is the geometric mean of its two neighbors, b=ac−−√ . Additionally,2b=x+y, 2x=a+b, and 2y=b+c
A term in an arithmetic progression is the arithmetic mean of its two neighboring terms — so in particular, b is the arithmetic mean of x and y. Note that the equation to be proved is equivalent to the statement “b is the harmonic mean of x and y.” Then by the this can only be true if b=x=y .Since a term in a geometric progression is the geometric mean of its two neighbors, b=ac−−√ . Additionally,2b=x+y, 2x=a+b, and 2y=b+cTherefore,
A term in an arithmetic progression is the arithmetic mean of its two neighboring terms — so in particular, b is the arithmetic mean of x and y. Note that the equation to be proved is equivalent to the statement “b is the harmonic mean of x and y.” Then by the this can only be true if b=x=y .Since a term in a geometric progression is the geometric mean of its two neighbors, b=ac−−√ . Additionally,2b=x+y, 2x=a+b, and 2y=b+cTherefore,4b=2x+2y=a+2b+c⟹2b=a+c⟹b=a+b2
A term in an arithmetic progression is the arithmetic mean of its two neighboring terms — so in particular, b is the arithmetic mean of x and y. Note that the equation to be proved is equivalent to the statement “b is the harmonic mean of x and y.” Then by the this can only be true if b=x=y .Since a term in a geometric progression is the geometric mean of its two neighbors, b=ac−−√ . Additionally,2b=x+y, 2x=a+b, and 2y=b+cTherefore,4b=2x+2y=a+2b+c⟹2b=a+c⟹b=a+b2But if b is both the arithmetic and geometric mean of a and c, then a=b=c , in which case x and y are also equal to b, as was to be proved.