A ball is dropped from a height of 512 m. It bounces back rising to a height of 256 m. each time it further touches the floor it rises to the half the height it fell from before the previous bounce. Find the total distance travelled by the ball.

Here's some information about arithmetic progressions (APs):  An AP is a sequence of numbers where the difference between any two consecutive numbers is constant.  Each term in an AP is derived from the preceding term by adding or subtracting a fixed number called the common difference.  The general form of an AP is \(a,a+d,a+2d,a+3d,...\).  The formula for the nth term of an AP is \(a=a+(n-1)\times d\).  The formula for the sum of the first n terms of an AP is \(S=n/2(2a+(n-1)\times d)\).  There are two main types of APs: Finite AP: An AP with a finite number of terms and a last... Show more

Here's some information about arithmetic progressions (APs): 
An AP is a sequence of numbers where the difference between any two consecutive numbers is constant. 
Each term in an AP is derived from the preceding term by adding or subtracting a fixed number called the common difference. 
The general form of an AP is \(a,a+d,a+2d,a+3d,...\). 
The formula for the nth term of an AP is \(a=a+(n-1)\times d\). 
The formula for the sum of the first n terms of an AP is \(S=n/2(2a+(n-1)\times d)\). 

There are two main types of APs:

Finite AP: An AP with a finite number of terms and a last term. 
Infinite AP: An AP with an infinite number of terms and no last term.

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