The total distance traveled by the ball is given by the expression[tex]S_n=\frac{n}{2}[2k+(n-1)(1.5k)][/tex]
The sequence that shows the distance rolled by the inclined plane in successive seconds is:
k, 2.5k, 4k, ................
The common difference d = 4k - 2.5k
The common difference, d = 1.5k
The first term, a = k
Let the number of terms be represented by n
The sum of n terms of an AP is given by the formula
[tex]S_n=\frac{n}{2}[2a+(n-1)d)[/tex]
Substitute a = k, d = 1.5k into the equation above
[tex]S_n=\frac{n}{2}[2k+(n-1)(1.5k)][/tex]
Learn more on sum of an AP here: https://brainly.com/question/24205483
