Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses
MATHEMATICAL
PRACTICESPractice Describe a pattern in each sequence. Then find the next two terms
of the sequence.
^P See Problem 1.- 6 ,13, 20, 27,...
- 10,4, - 2 , - 8 ,...
- 1.1, 2.2, 3.3, 4.4,...
- 8 , 4 ,2 ,1 ,...
- 13,11,9,7,...
- 99, 88, 77, 66,...
- 2, 6 ,1 0 , 14,...
- 2, 20, 200, 2000,...
- 4.5,9, 18,36,...
Tell whether the sequence is arithmetic. If it is, identify the common difference. 4P See Problem 2.- -9, -17, -26, -33,.
22 i 2’ 3’ 6' u' •- - o - -7 , -3,1, 5 ,...
- 2,11,21,32,...
- 10, 8, 6, 4,... 25. 10, 24, 36, 52,...
- 15,14.5, 14,13.5,13,... 28. 4, 4.4, 4.44, 4.444,
Write a recursive formula for each sequence.- 1.1, 1.9, 2.7, 3.5,... 31. 99, 88, 77, 6 6 ,...
- 13,10, 7, 4,... 34. 2.3, 2.8, 3.3, 3.8,..
20. 19,8, -3 , -1 4 ,...
23. 0.2,1.5,2.8, 4 .1 ,...
26. 3, 6 , 1 2 , 2 4 ,...
29. -3 ,-7 ,-1 0 ,-1 4 ,...
See Problem 3.- 23, 38, 53, 68,...
- 4.6, 4.7, 4.8, 4 .9 ,...
- Garage After one custom er buys 4 n ew tires, a garage recycling b in h as 20 tires ^ p See Problem 4.
in it. After a n o th e r custom er buys 4 n ew tires, th e b in has 24 tires in it. Write
an explicit form ula to re p resen t th e n u m b e r of tires in th e b in as a n arithm etic
sequence. How m any tires are in th e b in after 9 custom ers buy all n ew tires? - Cafeteria You have a cafeteria card w orth $50. After you buy lu n ch o n M onday,
its value is $46.75. After you buy lu n ch o n Tuesday, its value is $43.50. W rite an
explicit form ula to rep resen t th e a m o u n t of m o n ey left on th e card as an arithm etic
sequence. W hat is the value of th e card after you buy 12 lunches?
Write an explicit formula for each recursive formula. See Problem 5.- A(n) = A{n - 1) + 12; A{ 1 ) = 1 2 39. A{n) = A{n - 1) + 3.4; A (l) = 7.3
- A{n) = A {n - 1) + 3; A(l) = 6 41. A{n) = A {n - 1) - 0.3; A (l) = 0.3
Write a recursive formula for each explicit formula. ^P See Problem 6.- A{n) = 5 + { n - 1)(3) 43. A(n) = 3 + ( n - l ) ( - 5 )
- A{ri) = - 1 + (n - l)(-2 ) 45. A(n) = 4 + (n - 1)(1)
Find the second, fourth, and eleventh terms of the sequence described by
each explicit formula.- A(n) = 5 + ( n - l)(-3 ) 47. A(n) = - 3 + (n - 1)(5)
- A(n) = -11 + (n - 1)(2) 49. A{n) = 9 + {n - 1)(8)
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PowerAlgebra.com j Lesso n 4- 7 A r i t h m e t i c Seq u en ces 279