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Geometric Progression

If k + 1, 3k ...

Question

If k + 1, 3k - 4, 2k + 3 are three successive terms of an A.P. then k =_____

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Solution

Given,

$k + 1, 3 k - 4, 2 k + 3$ are in A.P.

$\Rightarrow 3 k - 4 - (k + 1) = 2 k + 3 - (3 k - 4)$

$3 k - 4 - k - 1 = 2 k + 3 - 3 k + 4$

$2 k - 5 = - k + 7$

$3 k = 12$

$∴ k = 4$

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