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Ungrouped Frequency Table

If k-3, 2k+...

Question

If $(k - 3), (2 k + 1)$ and $(4 k + 3)$ are three consecutive terms of an A.P., find the value of k.

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Solution

Since these terms are consecutive terms of an A.P., the middle term must be the average of the other two.
$\Rightarrow (k - 3) + (4 k + 3) = 2 (2 k + 1)$
$\Rightarrow 5 k = 4 k + 2$
$\Rightarrow k = 2$
Thus, the required value of k is 2.

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