Bean sprouts grow very quickly. A bean sprout has grown to a height of 5 millimetrs. Tomorrow it will be 14 millimeters tall, the next day it will be 23 millimeters tall, and on the next day it will be 32 millimeters tall.
Part 1) Write a rule to represent the height of the bean sprout as an arithmetic sequence.
(1 point)
Responses
A(n) = 5 + (n - 1) 9
A(n) = 5 + (n - 1) 9
A(n) = 14 + (n - 1)9
A(n) = 14 + (n - 1)9
A(n) = 5 - (n - 1)9
A(n) = 5 - (n - 1)9
A(n) = 9n
A(n) = 9n
A(n) = 9 + (n + 1)5
A(n) = 9 + (n + 1)5
Question 2
Part 2) How tall will the bean sprout be in 12 days? (1 point)
Responses
108 millimeters
108 millimeters
113 millimeters
113 millimeters
74 millimeters
74 millimeters
94 millimeters
94 millimeters
104 millimeters
To solve this problem, we need to find the common difference in the arithmetic sequence. We can do this by subtracting the previous term from the current term.
From the information given, we can see that the common difference is 9 because each day, the height increases by 9 millimeters.
Using the formula for the nth term of an arithmetic sequence:
A(n) = a_1 + (n-1)d
where A(n) is the nth term, a_1 is the first term, n is the number of terms, and d is the common difference.
In this case, the first term is 5 millimeters and the common difference is 9 millimeters.
Therefore, the rule to represent the height of the bean sprout as an arithmetic sequence is:
A(n) = 5 + (n-1)9
Now, to find the height of the bean sprout in 12 days, we can substitute n=12 into the formula:
A(12) = 5 + (12-1)9
A(12) = 5 + 11*9
A(12) = 5 + 99
A(12) = 104 millimeters
So the bean sprout will be 104 millimeters tall in 12 days.