Mathematics, 18.07.2019 16:30 monicorequena7

Determine if the sequence is arithmetic. if it is, find the common difference. is the sequence a function ? 6.) -7, -10, -11, -13, determine if the sequence is geometric. if it is, find the common ratio 8.) 4, 20, 100, 500, 10.) -30, -45, -50, -65, determine if the sequence is geometric. if it is, find the common ratio. is the sequence a function? 12.) -7, -14, 21, -28,

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Common difference exists if the difference between any two consecutive values in a sequence is the same while common ratio exists if the ratio between any two consecutive values In a sequence are the same.

Common ratio = r2/r1 = r3/r2 = r4/r3... Common difference = d2 - d1 = d3 - d2...

1.)

For the sequence : -7, -10, -11, -13,

-10 - (-7) = - 11 - (-10)

-10 + 7 = - 11 + 10

-3 ≠ - 1

Hence, the sequence is not arithmetic

2.)

For the sequence : 4, 20, 100, 500

20/4 = 100/20 = 500/100

5 = 5 = 5

Hence, the sequence is geometric

3.) For the sequence : 30, -45, -50, -65

-45/30 ≠ - 50/45 ≠ - 65/50

Hence, the sequence is not geometric

4.)

For the sequence : -7, -14, 21, -28, ...

-14 - (-7) = 21 - (-14)

-14 + 7 = 21 + 14

-7 ≠ 35

Hence, the sequence is not arithmetic

Therefore, arithmetic and geometric sequences do have a common difference and common ratio respectively.

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Answer from: jorell

$6)\\r=a_{n+1}-a_n\to r=a_2-a_1=a_3-a_2=a_4-a_3=...\\\\a_1=-7;\ a_2=-10;\ a_3=-11;\ a_4=-13\\\\a_2-a_1=-10-(-7)=-10+7=-3\\a_3-a_2=-11-(-10)=-11+10=-1\\\\a_3-a_2\neq a_2-a_1\\\\\text{It's not an arithmetic sequence}$

$\r=\dfrac{a_{n+1}}{a_n}\\\\r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...\\\\8.)\\a_1=4;\ a_2=20;\ a_3=100;\ a_4=500\\\\r=\dfrac{20}{4}=\dfrac{100}{20}=\dfrac{500}{100}=5\\\\10.)\\a_1-30;\ a_2=-45;\ a_3=-50;\ a_4=-65\\\\\dfrac{a_2}{a_1}=\dfrac{-45}{-30}=\dfrac{3}{2}\\\\\dfrac{a_3}{a_2}=\dfrac{-50}{-45}=\dfrac{10}{9}\\\\\dfrac{a_2}{a_1}\neq\dfrac{a_3}{a_2}\\\\\text{It's not a geometric sequence}$
$12.)\\a_1=-7;\ a_2=-14;\ a_3=-21;\ a_4=-28\\\\\dfrac{a_2}{a_1}=\dfrac{-14}{-7}=2\\\\\dfrac{a_3}{a_2}=\dfrac{-21}{-14}=\dfrac{3}{2}\\\\\dfrac{a_2}{a_1}\neq\dfrac{a_3}{a_2}\\\\\text{It's not a geometric sequence}\\\\\text{It's a function}$

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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Answer from: Quest

step-by-step explanation:

$\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\\dfrac{m^7n^3}{mn^{-1}}=m^{7-1}n^{)}=m^6n^4$

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Determine if the sequence is arithmetic. if it is, find the common difference. is the sequence a fun...