properties of an a.p.

Asked by nmenghani | 30th May, 2011, 05:49: PM

Expert Answer:

Note : x, y, z are in AP iff : x + z = 2y .......... (1)
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? 1/a, 1/b, 1/c are in AP

? (1/a) + (1/c) = 2(1/b)

? (c+a) / (ca) = 2/b

? b(c+a) = 2(ca)

? (bc+ab) = 2(ca) ................... (2)
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Then, we have :

... a(b+c) + c(a+b)

= ab + ca + ca + bc

= (bc+ab) + 2(ca)

= (bc+ab) + (bc+ab) ............ from (2)

= 2(bc+ab)

= 2 · b(c+a)
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? a(b+c) + c(a+b) = 2 · b(c+a)

? from (1),

... a(b+c), b(c+a), c(a+b) are in AP.

Answered by  | 30th May, 2011, 05:38: PM

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