Question:
The first three terms in a G.P. are $a, b$ and $c$ where $a \neq b$. Then the fifth term is:
The first three terms in a G.P. are $a, b$ and $c$ where $a \neq b$. Then the fifth term is:
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For any three consecutive terms $x, y, z$ in G.P., $y^2 = xz$.
Updated On: Apr 28, 2026
- $\frac{c^{2}}{2a}$
- $\frac{c}{2a}$
- $\frac{c^{2}}{a}$
- $\frac{c^{2}}{3a}$
- $\frac{c}{3a}$
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The Correct Option is C
Solution and Explanation
Step 1: Analysis
In a G.P., the common ratio is $r = \frac{b}{a} = \frac{c}{b}$. Also, $b^2 = ac$.
Step 2: Formula
The fifth term is $a_5 = ar^4$.
Step 3: Calculation
$a_5 = a(\frac{c}{b})^4 = a \frac{c^4}{(b^2)^2}$. Substituting $b^2 = ac$: $a_5 = a \frac{c^4}{(ac)^2} = a \frac{c^4}{a^2 c^2} = \frac{c^2}{a}$. Final Answer: (C)
In a G.P., the common ratio is $r = \frac{b}{a} = \frac{c}{b}$. Also, $b^2 = ac$.
Step 2: Formula
The fifth term is $a_5 = ar^4$.
Step 3: Calculation
$a_5 = a(\frac{c}{b})^4 = a \frac{c^4}{(b^2)^2}$. Substituting $b^2 = ac$: $a_5 = a \frac{c^4}{(ac)^2} = a \frac{c^4}{a^2 c^2} = \frac{c^2}{a}$. Final Answer: (C)
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