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i got an answer but i would like to know how to get it by using a formula?

__The exercise gose like this:__

**Initially, a pendulum swings through an arc of 2feet. On each successive swing,the length of the arc is 0.9 of the previous length.**

**a. Determine the lenght of the arc after 10 swings**

__i did this to find the answer:__

using the formula Sn= a((r^n)-1)/r-1 were

Sn=?

a=2

r=0.9

n=10

Sn=2((0.9^10)-1)/0.9-1

Sn= 13.03 feet.

__the aswer will be 13.03 feet__

**B. On which swing is the lenght of the arc first less than 1 foot?**

I got that it was on the 7th swing were it is 0.9565938. but i got it by multipliying the 2feet by 0.9 and then its answer x 0.9 egain and so on ...until it give me an answer lower than 1...

how can i get this by using a formula(wich formula should i use) ??

**C. After the 15 swings,Determine the total lenght that the pendulum will have swung.**

using the same formula as

**a**I can get this answer but rather than using n=10 it will be n=15

right??

thanks in advance for ur help.