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## Answers

**ANSWER: k = 2**

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Equate the ratio:

3k + 4 7k + 6

---------- = -----------

2k + 1 3k + 4

(3k + 4) (3k +4) = (2k + 1) (7k + 6)

9k² + 24k + 16 = 14k² + 12k + 7k + 6

14k² - 9k² + 19k - 24k + 6 - 16 = 0

5k² - 5k - 10 = 0

Solve for k by factoring method:

(5k + 5) (k - 2) = 0

5k + 5 = 0 k - 2 = 0

5k = -5

**k = 2**

5k/5 = -5/5

**k = -1**

If

**k = 2,**the geometric sequence is:

**5, 10, 20**

2k + 1 ⇒ 2(2) + 1 = 5

3k + 4 ⇒ 3(2) + 4 = 10

7k + 6 ⇒ 7(2) + 6 = 20

**The common ratio is 2:**

10/5 = 2

20/10 = 2