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!


Comments

Post a Comment

Popular posts from this blog

Matching Type. Choose The Correct Answer From The Selection., In This Motion Over The Course Of The Year, It Has Been Observed That The Sun Appears To

Matching Type. Choose the correct answer from the selection. In this motion over the course of the year, it has been observed that the Sun appears to move a little towards the East each day as seen with respect to the background stars. Answer 1 Planets moved on small epicycles which in turn moved uniformly on circular orbits that were not centered on the sun. Answer 2 In astronomy, a(n) ____________ is a smaller circle whose center is located on the circumference of another larger circle. Answer 3 The model of the universe in which each planet moves uniformly counter-clockwise on a circle called the epicycle. Answer 4 This theory compromised the Ptolemaic and Copernican systems and avoided the problems of a moving Earth. Answer 5 Form of the moon when spring tide occurs Answer 6 He came up with a radical way of looking at the universe through the heliocentric system. Answer 7 A student of Plato who believed in a geocentric universe and that the planets
Read more

Which Species Is Most Likely To Exhibit Clumped Dispersion?, A. , Dandelions With Seeds Dispersed By The Wind, B. , Tigers That Defend Their Territori

Which species is most likely to exhibit clumped dispersion? A. dandelions with seeds dispersed by the wind B. tigers that defend their territories from one another C. a bird that nests in many different types of trees D. a tree that grows only on the banks of streams   Which species is most likely to exhibit clumped dispersion? A.dandelions with seeds dispersed by the wind B.tigers that defend their territories from one another C.a bird that nests in many different types of trees D.a tree that grows only on the banks of streams The answer is letter B.  tigers that defend their territories from one another. Here are the explanation. Clumped dispersion is when there is a clustering of individuals in a  group, producing some patches with several individuals and some patches with no individuals.   Individuals are spaced evenly across  an area, in uniform dispersion.  And the individuals are distributed in  random dispersion without any apparent pattern.
Read more