Mathematics: Aball rolling down an inclined plane travels, in successive seconds, k feet, 2.5k feet, 4k feet, etc… . find the distance traveled by the ball

I guess its C, not sure though...

Aball rolling down an inclined plane travels, in successive

elisaalonso8805

10.03.2022

The total distance traveled by the ball is given by the expression $S_n=\frac{n}{2}[2k+(n-1)(1.5k)]$

Finding distance using the sum of an AP

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

$S_n=\frac{n}{2}[2a+(n-1)d)$

Substitute a = k, d = 1.5k into the equation above

$S_n=\frac{n}{2}[2k+(n-1)(1.5k)]$

Learn more on sum of an AP here: link

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