bean plants grow rapidly. a bean plant is 16 inches tall. Tomorrow it will be 24 inches tall, the next day it will be 32 inches tall and on the next day it will be 40 inches tall. Write a rule to represent the heights of the bean plant as an arithmetic sequence. how tall will the plant be in 12 days?
A(n) = 16+(n-1)8;104 inches
A(n) = 16+(n-1)8;116 inches
A(n) = 16n; 192 inches****
A(n) = 12n; 144 inches
please help I am confused with this one
ok thanks
To represent the heights of the bean plant as an arithmetic sequence, we can use the formula: A(n) = a + (n-1)d, where A(n) represents the height of the bean plant on the nth day, 'a' represents the initial height of the bean plant, 'n' represents the number of days, and 'd' represents the common difference between each term (which in this case is 8 inches).
Given that the initial height of the bean plant is 16 inches, the formula becomes:
A(n) = 16 + (n - 1)8
To find the height of the bean plant in 12 days, substitute 'n' as 12 into the formula:
A(12) = 16 + (12 - 1)8
A(12) = 16 + 11 * 8
A(12) = 16 + 88
A(12) = 104
Therefore, the bean plant will be 104 inches tall in 12 days.
To represent the heights of the bean plant as an arithmetic sequence, we need to find a rule that relates the term number (n) to the corresponding height of the plant.
Notice that each day, the bean plant grows by an additional 8 inches. So, for each day, the height increases by 8 inches.
Now, let's analyze the given information:
- The initial height of the bean plant is 16 inches.
- On the next day, it increases by 8 inches, making it 24 inches.
- On the day after, it increases by another 8 inches, making it 32 inches.
- And on the next day, it increases by another 8 inches, making it 40 inches.
From this information, we can see that the difference (common difference) between two consecutive terms in the arithmetic sequence is 8.
Now, let's write the rule for the heights of the bean plant:
A(n) = 16 + (n-1)8
- Here, A(n) represents the height of the bean plant at term number n.
- The first term in the sequence is 16.
- The common difference is 8.
- (n-1) represents the number of terms that have passed since the initial height of 16 inches.
To find the height of the bean plant in 12 days, substitute n = 12 into the rule:
A(12) = 16 + (12-1)8
A(12) = 16 + 11*8
A(12) = 16 + 88
A(12) = 104 inches
Therefore, the height of the bean plant after 12 days will be 104 inches.