Grass seeds grow rapidly. A grass seed has grown to a 12 millimeter tall blade of grass. 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 blade of grass as an arithmetic sequence. How tall will the blade of grass be in 15 days?
In an arithmetic sequence, each term is found by adding a constant value to the previous term. Looking at the given sequence, each day the height of the grass increases by a fixed amount. To find this amount, we can calculate the difference between any two consecutive days:
Height on second day - Height on first day = 23 mm - 12 mm = 11 mm
Height on third day - Height on second day = 34 mm - 23 mm = 11 mm
Height on fourth day - Height on third day = 45 mm - 34 mm = 11 mm
Each day, the grass grows by 11 millimeters. Therefore, the rule for the height of the blade of grass as an arithmetic sequence is:
Height_n = Height_1 + (n - 1) * d
Where:
Height_n is the height on the nth day
Height_1 is the initial height on the first day, which is 12 mm
n is the day number
d is the common difference between the heights, which is 11 mm
To find out the height of the grass on the 15th day, we can plug the values into the formula:
Height_15 = Height_1 + (15 - 1) * d
Height_15 = 12 mm + (14) * 11 mm
Height_15 = 12 mm + 154 mm
Height_15 = 166 mm
Therefore, the blade of grass will be 166 millimeters tall on the 15th day.