For a science experiment Dana tracks the height of a plant I

For a science experiment, Dana tracks the height of a plant. Initially, the plant is 3 cm tall. If the plant grows at a rate of 1.5 cm per day, how long will it take for the plant to reach a height of 21 cm?

Solution

Initially the plant is 3 cm, and we want plant to reach height of 21cm

we can write it as an arithmetic sequence of form x_n=a+(n-1)d

where a=3cm , d=1.5cm , x_n=21cm , n=?

21=3+(n-1)*1.5

21-3=(n-1)*1.5 => 18/1.5=n-1 => 12+1=n => n=13

So, it will take plant 13 days to reach height of 21cm