Grass seeds grow reapidly. A grass seed has grown to a 12 millimeter tall blade of grass tommrrow 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 blade of grass as an arithmtic sequence. How tall will the blade of grass be in 15 days?
A. A(n) = 16 + (n - 1) 11; 194 millimeters
B. A(n) = 12 + 9n-1) 11; 166 millimeters
C. A(n) = 13n; 195 millimeters
D. A(n) = 12n; 180 millimeters
The correct answer is A. A(n) = 16 + (n - 1) 11; 194 millimeters.
To find the rule for the arithmetic sequence, we need to identify the common difference. We can do this by subtracting each term from the previous term:
23 - 12 = 11
34 - 23 = 11
45 - 34 = 11
Since the difference is consistent at 11, we know that the common difference is 11.
To find the formula for the nth term (A(n)), we can use the formula A(n) = A(1) + (n - 1)d, where A(1) is the first term and d is the common difference.
In this case, the first term (A(1)) is 12 and the common difference (d) is 11.
Plugging these values into the formula, we get:
A(n) = 12 + (n - 1)11
Finally, to find the height of the blade of grass in 15 days, we substitute n = 15 into the formula:
A(15) = 12 + (15 - 1)11
A(15) = 12 + 14 * 11
A(15) = 12 + 154
A(15) = 166 millimeters
Therefore, the height of the blade of grass in 15 days will be 166 millimeters.