Question:
If \( (2x - 1), 7, 3x \) are in A.P., then what is the value of \( x \)?
If \( (2x - 1), 7, 3x \) are in A.P., then what is the value of \( x \)?
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In an A.P., the middle term is the arithmetic mean of the terms on either side.
Updated On: Oct 27, 2025
- \( 3 \)
- \( 4 \)
- \( 1 \)
- \( 5 \)
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The Correct Option is A
Solution and Explanation
For three numbers to be in A.P., the middle term is the average of the others:
\[ 7 - (2x - 1) = 3x - 7 \] Expanding: \[ 7 - 2x + 1 = 3x - 7 \] \[ 8 - 2x = 3x - 7 \] \[ 8 + 7 = 3x + 2x \] \[ 15 = 5x \Rightarrow x = 3. \]
\[ 7 - (2x - 1) = 3x - 7 \] Expanding: \[ 7 - 2x + 1 = 3x - 7 \] \[ 8 - 2x = 3x - 7 \] \[ 8 + 7 = 3x + 2x \] \[ 15 = 5x \Rightarrow x = 3. \]
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