Question:
If \( 1, a, b, c, 16 \) are in geometric progression, then \( \sqrt[3]{abc} \) is equal to
If \( 1, a, b, c, 16 \) are in geometric progression, then \( \sqrt[3]{abc} \) is equal to
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In GP, expressing terms as powers of the common ratio \( r \) makes multiplication and root calculations very simple.
Updated On: Apr 28, 2026
- \( 1 \)
- \( 2 \)
- \( 6 \)
- \( 4 \)
- \( 8 \)
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The Correct Option is D
Solution and Explanation
Step 1: Represent the GP using first term and common ratio.
Let the common ratio be \( r \). Then the sequence becomes: \[ 1, r, r^2, r^3, r^4 \] So, \[ a = r,\quad b = r^2,\quad c = r^3 \]
Step 2: Use the last term to find \( r \).
Given: \[ r^4 = 16 \] \[ r = \sqrt[4]{16} = 2 \]
Step 3: Find values of \( a, b, c \).
\[ a = 2,\quad b = 4,\quad c = 8 \]
Step 4: Compute the product \( abc \).
\[ abc = 2 \cdot 4 \cdot 8 = 64 \]
Step 5: Take cube root.
\[ \sqrt[3]{abc} = \sqrt[3]{64} \]
Step 6: Simplify the cube root.
\[ \sqrt[3]{64} = 4 \]
Step 7: Final conclusion.
Thus, the required value is: \[ \boxed{4} \] Correct option is: \[ \boxed{(4)\ 4} \]
Let the common ratio be \( r \). Then the sequence becomes: \[ 1, r, r^2, r^3, r^4 \] So, \[ a = r,\quad b = r^2,\quad c = r^3 \]
Step 2: Use the last term to find \( r \).
Given: \[ r^4 = 16 \] \[ r = \sqrt[4]{16} = 2 \]
Step 3: Find values of \( a, b, c \).
\[ a = 2,\quad b = 4,\quad c = 8 \]
Step 4: Compute the product \( abc \).
\[ abc = 2 \cdot 4 \cdot 8 = 64 \]
Step 5: Take cube root.
\[ \sqrt[3]{abc} = \sqrt[3]{64} \]
Step 6: Simplify the cube root.
\[ \sqrt[3]{64} = 4 \]
Step 7: Final conclusion.
Thus, the required value is: \[ \boxed{4} \] Correct option is: \[ \boxed{(4)\ 4} \]
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