1. **State the problem:** We need to find the value of $k$ such that the terms $2k+7$, $6k-2$, and $8k-4$ form an arithmetic progression (AP). 2. **Recall the property of an AP:** In an arithmetic progression, the difference between consecutive terms is constant. This means: $$ (6k - 2) - (2k + 7) = (8k - 4) - (6k - 2) $$ 3. **Set up the equation:** $$ (6k - 2) - (2k + 7) = (8k - 4) - (6k - 2) $$ 4. **Simplify both sides:** Left side: $$ 6k - 2 - 2k - 7 = 4k - 9 $$ Right side: $$ 8k - 4 - 6k + 2 = 2k - 2 $$ 5. **Equate and solve for $k$:** $$ 4k - 9 = 2k - 2 $$ Subtract $2k$ from both sides: $$ 2k - 9 = -2 $$ Add 9 to both sides: $$ 2k = 7 $$ Divide both sides by 2: $$ k = \frac{7}{2} $$ 6. **Final answer:** $$ k = 3.5 $$