1. Geometric & Arithmetic
By: Kasey Rosser, Stormy Smith, & Bryson Starks

2. Arithmetic Sequence Question
You visit the Grand Canyon and drop a penny off the edge of a cliff. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and so on. What is the total distance the penny will fall in 6 seconds?

3. Answer! Sequence: 16, 48, 80, …. Sn = n(a1 + an )/2
an = a1 + d(n-1) S6 = 6(16+176)/2
a6 = (6-1) S6= 576 feet
a6 = 176

4. Arithmetic Series
A theater has 60 seats in the first row, 68 seats in the second row, 76 seats in the third row, and so on.  If the theater has 20 rows of seats, how many seats are in the theater?

5. Answer!
Arithmetic sequence: 60, 68, 76, Sn= n(a1+an)/2 Find the sum: S20= 20(60+212)/2 n = 20,  a1 = 60,  d = 8 and we need  S20= 2720
a20  an= a1+d(n-1)
a20=60+8(20-1)
a20=212

6. Geometric Sequence
A culture of bacteria doubles every 2 hours. If there are 500 bacteria at the beginning, how many bacteria will there be after 24 hours?

7. Answer! an = a1 + (n-1) an = a1 *r ^(n-1)

8. Geometric Series
Xavier is on a swing and is given a big push. He goes 6 feet on the first swing but only half as far every other swing. How far (total distance) does he travel before the swing stops?

9. Answer!
S=a1/ 1-r S=6/(1-(1/2)) a1= 6 ft. S=6/(1/2) r=1/2 S=12*(2) S=12 ft.

10. Movie Time!