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

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Solution

Step 1. Given:
Three consecutive terms are $a_{1} = (k - 3), a_{2} = (2 k + 1), a_{3} = (4 k + 3)$ .
Step 2. Find the value of $k$ :
Since these terms are consecutive terms of an A.P., the middle term must be the average of the other two.
That is, $a_{2} = \frac{a_{1} + a_{3}}{2}$
$\Rightarrow 2 k + 1 = \frac{k - 3 + 4 k + 3}{2} \Rightarrow 4 k + 2 = 5 k \Rightarrow k = 2$
Therefore, the required solution is $k = 2$ .

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