FIITJEE A.I.T.S mains level

Algebra Level 4

Given that
i) $a,b,c$ follows an arithmetic progression.
ii) $b,c,d$ follows a geometric progression.
iii) $c,d,e$ follows a harmonic progression.

Then $a,c,e$ follows a:

None of these choices Harmonic progression Geometric progression Arithmetic progression

1 solution

Akshat Sharda
Oct 16, 2015

$\text{a,b,c are in A.P.}\Rightarrow 2b=a+c \\ \text{b,c,d are in G.P.}\Rightarrow c^{2}=b \cdot d \\ \text{c,d,e are in H.P.}\Rightarrow \frac{2}{d}=\frac{1}{c}+\frac{1}{e} \\ \Rightarrow \frac{2}{d}=\frac{1}{c}+\frac{1}{e}\Rightarrow \frac{2}{\frac{c^{2}}{b}}=\frac{c+e}{ce} \\ \Rightarrow \frac{2b}{c}=\frac{c+e}{e}\Rightarrow \frac{a+c}{c}=\frac{c+e}{e} \\ \Rightarrow c^{2}=ae \Rightarrow \text{Therefore, a,c,e are in G.P.}$

FIITJEE A.I.T.S mains level

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