If a , b , c are in H.P., then b − c a − b is equal to

b = a + c 2 a c . Then b − c a − b = a + c 2 a c − c a − a + c 2 a c = a c − c 2 a 2 − a c = c ( a − c ) a ( a − c ) = c a .

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MathematicsSequence & SeriesH.P.Medium2 minQB

MathematicsMediumsingle choice

If $a, b, c$ are in H.P., then $\frac{a - b}{b - c}$ is equal to

Options:

Answer:

Solution:

$b = \frac{2 a c}{a + c}$ . Then $\frac{a - b}{b - c} = \frac{a - \frac{2 a c}{a + c}}{\frac{2 a c}{a + c} - c} = \frac{a ^{2} - a c}{a c - c ^{2}} = \frac{a ( a - c )}{c ( a - c )} = \frac{a}{c}$ .

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

⏱ 2mℹ️ Source: QB

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