Flowers grow rapidly. A flower is 60 inches tall. Tomorrow it will be 71 inches tall. The next day it will be 82 inches tall,and on the next day it will be 93 inches tall. Write a rule to represent the height of the flower as an arithmetic sequence. How tall will the plant be in 12 days?
Let's assume that the initial height of the flower is h inches, where h is a variable.
Using the given information, we can set up an arithmetic sequence with a common difference of 11 inches (the difference in height between each day).
The heights of the flower on each day can be represented by the arithmetic sequence: h, h + 11, h + 22, h + 33, ...
To find the general formula for the height of the flower on any given day, we can observe that the difference between each term in the sequence is constant (11 inches). This means that the formula for the nth term of the arithmetic sequence (an) can be written as:
an = h + (n - 1)d
where n represents the day number and d represents the common difference (11 inches).
Using this formula, we can find the height of the flower on any given day.
For example, on the 3rd day (n = 3), the height of the flower (a3) can be calculated as:
a3 = h + (3 - 1)11
= h + 22
Similarly, on the 12th day (n = 12), the height of the flower (a12) can be calculated as:
a12 = h + (12 - 1)11
= h + 11(11)
= h + 121
Therefore, the height of the plant in 12 days would be h + 121 inches.