If k + 7, $2k - 2$ and $2k + 6$ are three consecutive terms of an A.P., then the value of k is

Step 1: Define terms of A.P.

Let the three consecutive terms of the Arithmetic Progression (A.P.) be $a_1$, $a_2$, and $a_3$. We are given these terms in terms of $k$.

Step 2: Apply A.P. property

In an Arithmetic Progression, the difference between any two consecutive terms is constant. This constant difference is known as the common difference. Therefore, the difference between the second and first term must be equal to the difference between the third and second term.

Step 3: Substitute the terms

Now, we substitute the given expressions for $a_1$, $a_2$, and $a_3$ into the A.P. property equation. This will give us an equation solely in terms of $k$.

Step 4: Simplify and solve for k

We simplify both sides of the equation by combining like terms. On the left side, $2k - k$ becomes $k$, and $-2 - 7$ becomes $-9$. On the right side, $2k - 2k$ cancels out, and $6 + 2$ becomes $8$. Finally, we isolate $k$ by adding $9$ to both sides.

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