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Bamboo plants grow rapidly. A bamboo plant is 130 inches tall. Tomorrow it will be 143 inches tall, the next day it will be 156 inches tall, and on the next day it will be 169 inches tall. Write a rule to represent the height of the bamboo plant as an arithmetic sequence. How tall will the plant be in 13 days?

Respuesta :

jaimie11121
well, (y for bamboo plant, x per day) y=130+13x  just use 13 for x for the second part. (It is 169+130. 299.)
TaeKwonDoIsDead

The sequence described is 130, 143, 156, 169, ...

To write the general formula/rule of the arithmetic sequence described above, we will use the the general term of arithmetic progressions formula:

[tex]T_{n}=a+(n-1)d[/tex]

Where,

  • a is the first term,
  • d is the common difference (difference in 2 terms)
  • n is the index of the term

Plugging in 130 as a and [tex]143-130=13[/tex] as d, we get,

[tex]T_{n}=130+(n-1)(13)\\ = 130 + 13n - 13\\=117+13n[/tex]

We can use this model to write our own rule:

[tex]H=117+13x[/tex]

Where,

  • H is the height of the bamboo plant, in inches
  • x is the day number, starting from x=1 as DAY 1

To find how tall the plant will be on Day 13, we plug in 13 for x in the formula and get,

[tex]H=117+13(13)=286[/tex] inches.


ANSWER:

Rule: [tex]H=117+13x[/tex] (H is height, in inches, and x is the Day Number)

13 days later, height of plant will be 286 inches.

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