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Mathematics - Sequence & Series Question with Solution | TestHub

MathematicsSequence & SeriesG.P.Medium2 minQB

MathematicsMediumsingle choice

Positive integers $a < b < c$ form a G.P. with natural-number ratio $r$ . If $b - a$ is the cube of a natural number and $lo g_{6} a + lo g_{6} b + lo g_{6} c = 6$ , find $a + b + c$ .

Options:

Answer:

Solution:

$ab c = 6^{6}$ and $ab c = b^{3}$ , so $b = 36$ . Thus $a = 36/ r$ is an integer and $b - a = 36 (r - 1) / r$ a positive cube. Checking the divisors $r > 1$ of 36 gives $r = 4$ , with $(a, b, c) = (9, 36, 144)$ and sum 189.

Stream:JEESubject:MathematicsTopic:Sequence & SeriesSubtopic:G.P.

⏱ 2mℹ️ Source: QB

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