Question:
If \( -5, k, -1 \) are in A.P., then the value of \( k \) is equal to:
If \( -5, k, -1 \) are in A.P., then the value of \( k \) is equal to:
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Another way to solve this is to ensure the common difference is equal: \( k - (-5) = -1 - k \). Solving \( k + 5 = -1 - k \) leads to \( 2k = -6 \), giving \( k = -3 \).
Updated On: May 6, 2026
- \( -5 \)
- \( -3 \)
- \( -1 \)
- \( 3 \)
- \( 5 \)
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The Correct Option is B
Solution and Explanation
Concept:
If three numbers \( a, b, c \) are in an Arithmetic Progression (A.P.), then the middle term is the arithmetic mean of the other two:
\[ b = \frac{a + c}{2} \]
Step 1: Apply the A.P. property to the given numbers.
Given \( a = -5 \), \( b = k \), and \( c = -1 \). \[ k = \frac{-5 + (-1)}{2} \]
Step 2: Simplify the expression.
\[ k = \frac{-6}{2} \] \[ k = -3 \]
Step 1: Apply the A.P. property to the given numbers.
Given \( a = -5 \), \( b = k \), and \( c = -1 \). \[ k = \frac{-5 + (-1)}{2} \]
Step 2: Simplify the expression.
\[ k = \frac{-6}{2} \] \[ k = -3 \]
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