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
I am guessing. Can you explain how the answer is a?
day1 = term1 = 16
day2 = term2 = 24 , an increase of 8
day3 = term3 = 32 , an increase of 8
looks like an arithmetic sequence where
a = 16, d = 8
so on day 12
we have term12
= a + 11d
= 16+11(8) = 104
somebody better call Jack
butts
So A ?
Yes,Chris.
somebody better call Saul instead of Jack he is the greatest attorney
thanks, I'm now flabbergasted but thank you! *☆(p≧w≦q)☆*
horace mann hate account
Of course! To determine the rule that represents the heights of the bean plant as an arithmetic sequence, we need to analyze the given information.
We are told that the bean plant's height is growing rapidly and that it starts at 16 inches. Additionally, we know that the height increases by 8 inches each day. This information suggests that the height of the bean plant forms an arithmetic sequence.
In an arithmetic sequence, the general formula is given as A(n) = a + (n-1)d, where "A(n)" represents the nth term of the sequence, "a" is the first term, "n" is the term number, and "d" is the common difference between each term.
Using the given information, we can substitute:
- "a" (the first term) as 16 inches (the initial height of the bean plant).
- "d" (the common difference) as 8 inches (the daily growth of the bean plant).
Using the formula, we get:
A(n) = 16 + (n-1)8.
Now, to determine the height of the bean plant in 12 days, we substitute "n" with 12 in the formula:
A(12) = 16 + (12-1)8.
Simplifying the equation:
A(12) = 16 + 11 * 8.
A(12) = 16 + 88.
A(12) = 104 inches.
Therefore, the correct answer is option A: A(n) = 16 + (n-1)8;104 inches.