Answers

  • Brainly User
2016-07-21T11:39:18+08:00
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

1 5 1