[tex]A(n)=12+(n-1)11\ ;\ 166\ \text{millimeters}[/tex]
It is given that:
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.
i.e. the first term of the arithmetic sequence is:
[tex]A(1)=12\\\\A(2)=23\\\\A(3)=34\\\\A(4)=45[/tex]
We know that the nth term of the sequence is given by:
[tex]A(n)=A(1)+(n-1)d[/tex]
where d is the common difference of the series.
Here the common difference is:
[tex]d=A(2)-A(1)\\\\i.e.\\\\d=23-12\\\\i.e.\\\\d=11[/tex]
Here we have the series as follows:
[tex]A(n)=12+(n-1)11[/tex]
Now, we are asked to find the height of the plant in 15 days.
i.e. n=15
Hence, we have:
[tex]A(15)=12+(15-1)\times 11\\\\i.e.\\\\A(15)=12+14\times 11\\\\i.e.\\\\A(15)=12+154\\\\i.e.\\\\A(15)=166\ \text{millimeters}[/tex]
