Question:
The 5th and 8th terms of a G.P. are 1458 and 54 respectively. The common ratio of the G.P. is
The 5th and 8th terms of a G.P. are 1458 and 54 respectively. The common ratio of the G.P. is
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Divide GP terms to eliminate \(a\) and directly solve for \(r\).
Updated On: May 8, 2026
- \( \frac{1}{3} \)
- \( 3 \)
- \( 9 \)
- \( \frac{1}{9} \)
- \( \frac{1}{8} \)
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The Correct Option is A
Solution and Explanation
Concept:
In G.P., \( T_n = ar^{n-1} \)
Step 1: Write expressions
\[ T_5 = ar^4 = 1458 \] \[ T_8 = ar^7 = 54 \]
Step 2: Divide equations
\[ \frac{ar^7}{ar^4} = \frac{54}{1458} \] \[ r^3 = \frac{54}{1458} \]
Step 3: Simplify fraction
\[ \frac{54}{1458} = \frac{1}{27} \] \[ r^3 = \frac{1}{27} \]
Step 4: Find \(r\)
\[ r = \frac{1}{3} \]
Step 5: Final answer
\[ \boxed{\frac{1}{3}} \]
Step 1: Write expressions
\[ T_5 = ar^4 = 1458 \] \[ T_8 = ar^7 = 54 \]
Step 2: Divide equations
\[ \frac{ar^7}{ar^4} = \frac{54}{1458} \] \[ r^3 = \frac{54}{1458} \]
Step 3: Simplify fraction
\[ \frac{54}{1458} = \frac{1}{27} \] \[ r^3 = \frac{1}{27} \]
Step 4: Find \(r\)
\[ r = \frac{1}{3} \]
Step 5: Final answer
\[ \boxed{\frac{1}{3}} \]
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