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

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?

Answer! Sequence: 16, 48, 80, …. Sn = n(a1 + an )/2 an = a1 + d(n-1) S6 = 6(16+176)/2 a6 = 16 + 32(6-1) S6= 576 feet a6 = 176

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?

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

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?

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

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?

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.

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