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

The correct answer is;

A(n) = 12 + (n-1)11; 166 millimeters

Step-by-step explanation:

Here, we want to write a rule representing the growth

From the question, we can see that the rate of growth is ;

34-23 = 23-12 = 11

This means it grows at a rate of 11 mm per day

So on the 15th day, its height will be;

We can have an arithmetic progression here, with 12 as the first term and 11 as the common difference

The nth term An can be represented as;

An = a + (n-1)d

where a = 12 mm , n = 15 and d = 11 mm

Thus, we have

An = 12 + (15-1)11

An = 12 + 154

An = 166 mm