Hello there,

I am suppose to answer this question but I don't know how to go about it.

A shrub 20cm tall is planted and in its first years it grow 8cm tall, in the second it grows 4cm more, in the third year it grows 2cm more and so on. What is the maximum height the tree will grow?

So far I have worked out that the height it continually grows is halved but I don't know what to do next. I want to do this manually without an aid of a calculator.
Thanks

Dear clueless123

There is a special homework board for this...

If the growth is halved every next year, you know the final total height, is it not?

20 + 8 + 4 + 2 + 1 + ( 0,5 + 0,25 + 0,125 + 0, 0625 + 0,03125 + 0,015625 + etc.)
As the increase gets smaller and smaller, the max. height is known. Just add the smaller amounts and round off... Better to use the algebraic formula for diminishing growth- see your textbook for that.

;)

This is a typical geometric series with common term r=1/2 and first term a_{1}=8.

Use the formula for a geometric series.

\frac{a_{1}}{1-r}

Then add what you get to the initial 20 inches/.