Question:
If three geometric means are inserted between 2 and 32, then the three numbers are
If three geometric means are inserted between 2 and 32, then the three numbers are
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For $n$ means, total terms = $n+2$.
Updated On: Apr 30, 2026
- $4,6,8$
- $6,8,10$
- $4,8,32$
- $4,6,12$
- $4,8,16$
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The Correct Option is
Solution and Explanation
Concept:
Insert GMs → form GP.
Step 1: Total terms
\[ 2, \_, \_, \_, 32 \] So 5 terms GP
Step 2: Find ratio
\[ 2r^4 = 32 \Rightarrow r^4 = 16 \Rightarrow r = 2 \]
Step 3: Find terms
\[ 2, 4, 8, 16, 32 \] Final Conclusion:
Inserted terms: $4,8,16$
Step 1: Total terms
\[ 2, \_, \_, \_, 32 \] So 5 terms GP
Step 2: Find ratio
\[ 2r^4 = 32 \Rightarrow r^4 = 16 \Rightarrow r = 2 \]
Step 3: Find terms
\[ 2, 4, 8, 16, 32 \] Final Conclusion:
Inserted terms: $4,8,16$
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