# Thread: Progression help

1. ## Progression help

I have seen questions like this many times but still unsure of doing it ..

Q: A ball rebounds to a height five-eighths of its previous height above the ground . If a ball is dropped from a height of 3 metres , find the total distance travelled by the ball before it comes to a rest ?

Is it a finite series or an infinite series ?

2. Originally Posted by thereddevils
I have seen questions like this many times but still unsure of doing it ..

Q: A ball rebounds to a height five-eighths of its previous height above the ground . If a ball is dropped from a height of 3 metres , find the total distance travelled by the ball before it comes to a rest ?

Is it a finite series or an infinite series ?
Its an infinite Geometric progression

Formula
$
S=\frac{a}{1-r}
$

'a' is the first term (3 in your case)
'r' is the common ratio ( $\frac{5}{8}$ in your case )

condition for using it
|r|<1

Go ahead

3. ## Re :

It forms a series as follows :

$3+2[1.875+1.875(\frac{5}{8})+1.875(\frac{5}{8})^2+...]$

$3+2[\frac{1.875}{1-\frac{5}{8}}]=13$

### a ball rebounds to a height five-eighths of its previous height above the ground

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