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# Geometric Series $S_n=\frac{a(r^n-1)}{r-1}$

1. 1
Find $S_8$ for the geometric series:
$$2+6+18+...$$
2. 2
Find $S_9$ for the geometric series:
$$-5+10-20+40-...$$
3. 3
Find the sum of the geometric series:
$$8000+4000+2000+...+125$$
4. 4
Find the sum of the geometric series:
$$-4+12-36+...+972$$
5. 5
Find the sum of the geometric series:
$$5+15+45+...+3645$$
6. 6
A ball bounces to 80% of its initial height. After its first bounce it reaches 4 metres.

a) Find the height after the 5th bounce.

b) Find the total distance traveled after it hits the ground for the 6th time. (to the nearest tenth).  Good test question!
7. 7
A ball bounces to 90% of its initial height. The ball is dropped from a height of 20 metres.

a) Find the height after the 6th bounce. (to the nearest hundredth)

b) Find the total distance traveled after it hits the ground for the 8th time. (to the nearest tenth)  Good test question!
8. 8
A ball bounces to 75% of its initial height. The ball is dropped from a height of 18 metres.

a) Find the height after the 4th bounce. (to the nearest tenth)

b) Find the total distance traveled after it hits the ground for the 5th time. (to the nearest tenth)  Good test question!

$$e=mc^2$$