Find $k$ given the consecutive arithmetic terms:
$k - 1, 2 k + 3, 7 - k$

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Solution

Since, $k - 1, 2 k + 3, 7 - k$ are in A.P

$\Rightarrow 2 k + 3 - k + 1 = 7 - k - 2 k - 32$

$k + 4 = 4 - 3 k$

$4 k = 0$

$∴ k = 0$

when $k = 0$ series is $- 1, 3, 7$

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