The correct answer is B) A(n) = 12 + (n – 1)11; 166 millimeters.
To find the rule for the height of the blade of grass as an arithmetic sequence, we can observe that the seed grows by 11 millimeters each day.
The initial height of the blade of grass is 12 millimeters, so the first term of the sequence is 12.
The common difference, which represents the amount the height increases each day, is 11.
Using the formula for an arithmetic sequence, A(n) = a + (n – 1)d, where A(n) represents the nth term of the sequence, a represents the first term, n represents the term number, and d represents the common difference, we can substitute the values.
A(n) = 12 + (n – 1)11
For the 15th day, we substitute n = 15 into the equation:
A(15) = 12 + (15 – 1)11
A(15) = 12 + 14 × 11
A(15) = 12 + 154
A(15) = 166
So, the blade of grass will be 166 millimeters tall in 15 days.
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?
(1 point)
A) A(n) = 16 + (n – 1)11; 194 millimeters
B) A(n) = 12 + (n – 1)11; 166 millimeters
C) A(n) = 13n; 195 millimeters
D) A(n) = 12n; 180 millimeters
1 answer