I want check A , B in two questions .

In the grand canyon question, part a) was done correctly but b) was not. Try summing the series again.

The next question is completely wrong, its not even an arithmetic series because the difference of consecutive terms is not constant. Try again.

 

You used the formula in part 1B incorrectly. And please, I can't stress enough how important it is to check if your answer seems reasonable.

The formula for a sum of an arithmetic series:

[tex]S_n=a+(a+d)+(a+2d)+...+(a+(n-1)d)=\frac{n}{2}\left(2a+(n-1)d\right)[/tex]

Since you're looking for the distance travelled in 9 seconds, you're looking for [itex]S_9[/itex]. You substituted [itex]n=T_9[/itex] rather than n=9.

And honestly, look at how ridiculous your answer seems: [itex]15+45+75+...+255 = 975,375[/itex]

So a penny falls 1 million feet in 9 seconds?