Flowers grow rapidly. A flower is 60 inches tall. Tomorrow it will be 71 inches tall. The next day it will be 82 inches tall, and on the next day it will be 93 inches tall. Write a rule to represent the height of the flower as an arithmetic sequence. How tall will the plant be in 12 days?

After 12 days, the plant will be 181 inches tall.

Step-by-step explanation:

Here the initial length of the plant = 60 inches

Let us assume the first term of the sequence in AP is a = 60

The growth next day = 71 inches = a2

So, the growth in 1 day = Final height - Initial height

= 71 in - 60 in = 11 inches

⇒ a (2) - a (1) = 11 inches

Also, the growth next day = 82 inches = a3

So, the growth 3rd day = 82 in - 71 in = 11 inches

⇒ a (3) - a (2) = 11 inches

⇒ a (3) - a (2) = a (2) - a (1)

So, the common difference d in the sequence = 11

So, the general term of an AP is given as a (n) = a + (n-1) d

Here, a (n) = 60 + (n-1) 11

Now, for n = 12

a (12) = 60 + (12-1) 11 = 60 + 11 (11)

= 60 + 121 = 181 inches

or, a (12) = 181 inches

Hence, after 12 days, the plant will be 181 inches tall.