Find k so that the numbers 2k+1,3k+4, and 7k+6 form a geometric sequnce.

Let a, b and c be in a geometric sequence, then ac = b^2

Hence, (2k + 1) (7k + 6) = (3k + 4) ^2

14k^2 + 19k + 6 = 9k^2 + 24k + 16

5k^2 - 5k - 10 = 0

5k^2 + 5k - 10k - 10 = 0

5k (k + 1) - 10 (k + 1) = 0

(5k - 10) (k + 1) = 0

5k - 10 = 0 or k + 1 = 0

5k = 10 or k = - 1

k = 2 or k = - 1

The geometric sequence formed is

2 (2) + 1, 3 (2) + 4, and 7 (2) + 6

5, 10, and 20

OR

2 (-1) + 1, 3 (-1) + 4, and 7 (-1) + 6

-1, 1, and - 1