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Quantitative Aptitude

A.M Greater than or Equal to G.M

If a, b, c ...

Question

If $a, b, c$ are the first three terms of a geometric series. If the harmonic mean of $a$ and $b$ is $12$ and that of $b$ and $c$ is $36$ , find the first five terms of the series.

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Solution

Let $a = \frac{b}{r}, c = b r$
So, the given information says $\frac{2 b^{2}}{b r + b} = 12$ and $\frac{2 b^{2} r}{b + b r} = 36$
Dividing the two, we get $r = 3$
Substituting the value of r in any one, we get b to be 24.
Thus, the first 5 terms of the series are $8, 24, 72, 216, 648.$

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If a,b,c are the first three terms of a geometric series. If the harmonic mean of a and b is 12 and that of b and c is 36, find the first five terms of the series.

Let a=br,c=brSo, the given information says 2b2br+b=12 and 2b2rb+br=36Dividing the two, we get r=3Substituting the value of r in any one, we get b to be 24.Thus, the first 5 terms of the series are 8,24,72,216,648.

If $a, b, c$ are the first three terms of a geometric series. If the harmonic mean of $a$ and $b$ is $12$ and that of $b$ and $c$ is $36$ , find the first five terms of the series.

Let $a = \frac{b}{r}, c = b r$
So, the given information says $\frac{2 b^{2}}{b r + b} = 12$ and $\frac{2 b^{2} r}{b + b r} = 36$
Dividing the two, we get $r = 3$
Substituting the value of r in any one, we get b to be 24.
Thus, the first 5 terms of the series are $8, 24, 72, 216, 648.$