Find the values of k, if the points A (k+1,2k) ,B (3k,2k+3) and C (5k-1,5k) are collinear.

Explanation

To find the values of \( k \) for which the points \( A(k+1, 2k) \), \( B(3k, 2k+3) \), and \( C(5k-1, 5k) \) are collinear, we can use the concept of the area of a triangle formed by these three points. If the area is zero, the points are collinear.

### Step-by-step Solution:

1. **Identify the coordinates of the points:**
- \( A = (k + 1, 2k) \)
- \( B = (3k, 2k + 3) \)
- \( C = (5k - 1, 5k) \)
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