Solution:

It is given that

k + 3, k + 2, 3k – 7 and 2k – 3 are in proportion

We can write it as

(k + 3) (2k – 3) = (k + 2) (3k – 7)

By further calculation

2k² – 3k + 6k – 9 = 3k² – 7k + 6k – 14

3k² – 7k + 6k – 14 – 2k² + 3k – 6k + 9 = 0

k² – 4k – 5 = 0

k² – 5k + k – 5 = 0

k(k – 5) + 1(k – 5) = 0

(k + 1) (k – 5) = 0

So,

k + 1 = 0 or k – 5 = 0

k = -1 or k = 5

Therefore, the value of k is -1, 5.