New grass seeds grow rapidly. A grass seed has grown to 12 millimeters tall. Tomorrow it will
be 23 millimeters tall, the next day it will be 34 millimeters tall, and on the next day it will be
45 millimeters tall. Write a rule to represent the height of the bean plant as an arithmetic
sequence. How tall will the plant be in 15 days?
A(n) = 16 + (n – 1)11; 194 millimeters
A(n) = 12 + (n – 1)11; 166 millimeters
A(n) = 13n; 195 millimeters
A(n) = 12n; 180 millimeters
It’s b , A(n) = 12 + (n – 1)11; 166 millimeters
It’s b , A(n) = 12 + (n – 1)11; 166 millimeters
Hmm, let me think about it for a moment... Ah, I've got it! The rule that represents the height of the bean plant as an arithmetic sequence is:
A(n) = 12 + (n – 1)11
So, if we plug in n = 15, we can find out how tall the plant will be in 15 days:
A(15) = 12 + (15 – 1)11
A(15) = 12 + 14 * 11
A(15) = 12 + 154
A(15) = 166 millimeters
So, the plant will be 166 millimeters tall in 15 days. Happy growing, little bean plant!
To represent the height of the grass seed as an arithmetic sequence, we need to find a rule that describes how the height changes over time.
In this case, the height of the grass seed increases by 11 millimeters each day. We can use the formula for an arithmetic sequence to represent the height of the grass seed as it grows:
A(n) = a + (n - 1)d
Where:
A(n) represents the height of the grass seed on the nth day,
a represents the initial height of the grass seed,
n represents the number of days,
and d represents the common difference between two consecutive terms in the sequence.
Given that the initial height of the grass seed is 12 millimeters, the formula becomes:
A(n) = 12 + (n - 1)11
Now, to find the height of the grass seed in 15 days, we substitute n = 15 into the formula:
A(15) = 12 + (15 - 1)11
= 12 + 14 * 11
= 12 + 154
= 166 millimeters
Therefore, the correct answer is:
A(n) = 12 + (n - 1)11; the height of the grass seed in 15 days will be 166 millimeters.
clearly, the sequence is
a = 12
d = 11
a_14 = 12 + 13*11 = ___