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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, ...

Respuesta :

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[tex]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}[/tex]


[tex]\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}[/tex]
[tex]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}[/tex]


fichoh

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.

Learn more :https://brainly.com/question/18479471

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