If $9 k - 6, 5 k - 4, 6 k - 17$ are in AP then the value of k is

- 3

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- 11

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3

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10

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Solution

The correct option is C $3$
Given that $9 k - 6, 5 k - 4, 6 k - 17$ are in A.P.

Therefore, the difference between the consecutive numbers is same.

Hence, $(5 k - 4) - (9 k - 6) = (6 k - 17) - (5 k - 4)$

$⟹ 5 k - 4 - 9 k + 6 = 6 k - 17 - 5 k + 4$

$⟹ 2 - 4 k = k - 13$

$⟹ 2 + 13 = k + 4 k$

$⟹ 5 k = 15$

$⟹ k = \frac{15}{5} = 3$

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