Limiting sum question? (1 Viewer)

[alice_dng]

This question is from maths in focus
A tree 3 m high grows by another 2 2/5 m after 5 years, then by another 1 23/25 m after 5 more years,
and so on, each year growing 4/5 more than the previous year’s growth. Find the ultimate height of the tree.

Please explain and show working out!
Thank you

 

[rolpsy]

which is an infinite geometric series, with a = 3 and r = 4/5

Using the limiting sum formula (noting that |a| < 1)

 

[braintic]

Just adding something to rolpsy's answer:
You might be confused by the 5 years. This actually doesn't play a part in the answer.
It takes 5 times longer to reach a particular height than if this growth was happening annually. Yet the ultimate height of the tree is the same in both cases.

 

[alice_dng]

Thank you both! Really helped