Find K So That The Numbers 2k+1, 3k+4, And 7k+6 Form A Geometric Sequence., A. 2; -1 , B. -2; 1 , C. 2; 1 , D. -2; -1

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

a. 2; -1
b. -2; 1
c. 2; 1
d. -2; -1

 

Answer:

A. 2, -1

Step-by-step explanation:

Geometric sequences have a common ratio (r) which can be obtained by dividing a term by the one before it.

r = \frac{a_{n}}{a_{n-1}}

\frac{3k + 4}{2k + 1} = tex\frac{7k + 6}{3k + 4}

Get rid of the denominators/cross-multiply.

(3k + 4)² = (7k + 6)(2k + 1)

9k² + 24k + 16 = 14k² + 19k + 6

0 = 14k² - 9k² + 19k - 24k + 6 - 16

0 = 5k² - 5k - 10

0 = k² - k - 2

Factor out.

0 = (k - 2)(k + 1)

k = 2, -1

Hope this helps!


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