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Common Difference

For what valu...

Question

For what values of $k$ will be $k + 9, 2 k - 1$ and $2 k + 7$ are the consecutive terms of AP.

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Solution

We know that for an AP, the difference between two consecutive terms is constant.
$\Rightarrow (2 k - 1) - (k + 9) = (2 k + 7) - (2 k - 1)$
$\Rightarrow k = 10 = 8$
$\Rightarrow k = 18$ .

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