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- Mathematical Patterns

Genesis C.

Sequence

A list of numbers that often form a pattern

Arithmetic sequence

A sequence whose successive terms differ by the same nonzero number d, called the common difference

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Arithmetic series

The indicated sum of the terms of an arithmetic sequence

Geometric sequence

A sequence in which the ratio of successive terms is a constant r, called the common ratio

Geometric series

The indicated sum of the terms of a geometric sequence

What to do if it asks to evaluate

Find the sum

Explicit formula

A formula that defines the nth term a/n or general term of a sequence as a function n

Recursive formula

A formula for a sequence in which one or more previous terms are used to generate the next term

Converge

An infinite series converges when the partial sums approach a fixed number

Diverge

An infinite series diverges when the partial sums do not to approach a fixed number

Series

The indicated sum of the terms of sequence

Common ratio

In a geometric sequence. The constant ratio of any term and the previous term

Common difference

In an arithmetic sequence the nonzero constant difference of any term and the previous term

Infinite sequence

A sequence with infinitely many terms

Finite

A sequence with a finite number of terms

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Summation notation

To denote the sum of a sequence defined by a rule

To find a given term where a/n is position. It is used in a sequence. It is arithmetic

Used to find the sum of the term given. Used for series. It is arithmetic

Used for finding a term in a sequence where n is the position. It is geometric

Used to find sum for a given term for a series. Used for series. Geometric

To calculate the sum for an infinite series when it is geometric andpasses convergence test

Has a sum only when r<1 and does this in infinite series

Converges

Has no sum and is when it isnt r<1. Usually arithmetic cant be caculated

Diverges

4.5+5.0+5.5+6.0+6.5=27.5

000.1, .0001, .00001. 720, 5040, 40,320

A1= 43. An = an-1. - 2. A6 =33. A1 = 6. An= an-1. -5. A5 = -14

1.no. 3.no. 5. Yes 3. 7. Yes. 4

11. 127. 13. 12.5. 15. 225. 17. -59

79. A1= -1 d=3. 81. A1=52. D= -10. 83. A1 = -100.5. D= 22

85. 9k + 32

28. Geometric. 720,1440. 31.arithmetic. 50,55. 34. Neither. 20, 26

48. 4. 50. 5/2. 51. 10. 59. 7

7. S8 = 32. 9. S8= 264. 11. S8 = 4,292

43. A40 = 300. 45. A1 = 34

1. S8 = 255. 3. S7 = 381. 5. S11= -10,235. 7. S8 = 255/256

24. Geometric. S10 = 2,046. 26. Geometric. S9 = -1,627,605. 28. Arithmetic. S1000 = 500,500

B

G

87. B. 88. I. 90. H. 92. 696. 61. A

1. Arithmetic d= 15. 4. Geometric. R = 0.5. 2. Geometric. R= 3. 5. Geometric. R= -0.5

9. Converges. Has sum. 12. Diverges. Has no sum. 15. Diverges. Has no sum

18. 11/9 or 1.2. 20. 5/6. 22. 9

41. 7/8. 42. 10

57. S7 = 140. 58. S11 = -825. 59. S25 = 1,375

1. Arithmetic. S30 = 900. 3. Geometric. S7 = -127 /16. 5. Geometric. S8 = 3,825/16

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