In which Progression ?

Algebra Level 3

If b + c 2 a a , c + a 2 b b , a + b 2 c c \dfrac{b + c - 2a}{a}, \dfrac{c + a - 2b}{b}, \dfrac{a + b - 2c}{c} are in A.P, then a , b , c a, b, c are in ?

Harmonic Progression Gometric Progression Arithmetic - Geometric Progression Arithmetic Progression

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1 solution

Samrit Pramanik
Oct 4, 2018

b + c 2 a a , c + a 2 b b , a + b 2 c c \dfrac{b+c-2a}{a},\dfrac{c+a-2b}{b},\dfrac{a+b-2c}{c} are in A.P.

b + c 2 a a + 3 , c + a 2 b b + 3 , a + b 2 c c + 3 \dfrac{b+c-2a}{a}+3,\dfrac{c+a-2b}{b}+3,\dfrac{a+b-2c}{c}+3 are also in A.P.

a + b + c a , a + b + c b , a + b + c c \dfrac{a+b+c}{a},\dfrac{a+b+c}{b},\dfrac{a+b+c}{c} are also in A.P.

1 a , 1 b , 1 c \dfrac{1}{a},\dfrac{1}{b},\dfrac{1}{c} are also in A.P.

i.e. a , b , c a,b,c are in H.P.(Harmonic Progression).

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