| If a, b, c, d and e are in continued proportion, then find out the value of \[\frac{a}{e}.\] |
A) \[\frac{{{a}^{3}}}{{{b}^{3}}}\]
B) \[\frac{{{b}^{3}}}{{{a}^{3}}}\]
C) \[\frac{{{a}^{4}}}{{{b}^{4}}}\]
D) \[\frac{{{a}^{5}}}{{{b}^{5}}}\]
Correct Answer: C
Solution :
| Since, a, b, c, d and e are in continued proportion. |
| \[\therefore \] \[\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{e}\] |
| \[\Rightarrow \] \[\frac{e}{d}=\frac{d}{c}=\frac{c}{b}=\frac{b}{a}\] |
| Now, \[c=\frac{{{b}^{2}}}{a}\] \[\left[ \because \frac{c}{b}=\frac{b}{a} \right]\] |
| \[\Rightarrow \] \[d=\frac{{{c}^{2}}}{b}=\frac{{{b}^{4}}}{{{a}^{2}}}\cdot \frac{1}{b}=\frac{{{b}^{3}}}{{{a}^{2}}}\] |
| \[\Rightarrow \] \[e=\frac{{{d}^{2}}}{c}=\frac{{{b}^{6}}}{{{a}^{4}}}\cdot \frac{a}{{{b}^{2}}}=\frac{{{b}^{4}}}{{{a}^{3}}}\] |
| \[\Rightarrow \] \[\frac{a}{e}=\frac{a}{({{b}^{4}}/{{a}^{3}})}=\frac{{{a}^{4}}}{{{b}^{4}}}\] |
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