Algebra 2/Trig1



|Formulas |

| an = a1 + d(n-1) | an = a1 r(n-1) | |

|Sn =[pic] |Sn = a1[pic] |[pic] |

Algebra 2/Trig: Sequence & Series Worksheet #1 Name Date

Find the pattern and tell whether the sequence is arithmetic, geometric, or neither.

1. 7, 10, 13, 16, … 2. 3, 6, 12, 24, …

pattern: pattern:

type: type:

3. 0, 1, 4, 9, 16, … 4. 4, -12, 36, –108, …

pattern: pattern:

type: type:

Write the first six terms of the sequence.

5. an = n2 - 1 6. an = 3n - 1 7. an = 5(-2)(n-1)

a1 = a1 = a1 =

a2 = a2 = a2 =

a3 = a3 = a3 =

a4 = a4 = a4 =

a5 = a5 = a5 =

a6 = a6 = a6 =

Write the next term and then write the rule (equation) for the nth term (an).

8. 5, 25, 125, 625, , … 9. 4, 10, 16, 22, , … 10. -1,-2,-3,-4, , …

11. 2, 6, 10, 14, , … 12. 1, [pic] 13. ½,1, 2, 4, 8, 16, , …

|Formulas |

| an = a1 + d(n-1) | an = a1 r(n-1) | |

|Sn =[pic] |Sn = a1[pic] |[pic] |

Write the rule for the sequence given the following.

14. r = 0.5, a1 = 10 15. d = 10, a1 = 1 16. 44, 22, 11,…

Determine the pattern, then write the rule (equation) for the following series.

Then find the sum. Write in sigma notation.

17. 6561 + 2187 + 729 + 243 + 81 + 27+ 9 + 3 + 1 18. 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12

Find the sum of the following series. Write in sigma notation.

19. [pic] Sum of the first 8 terms. 20. [pic] Sum of the first 25 terms.

Find the sum of the series. (For larger series find the pattern & use the Sn formulas.)

21. [pic] 22. [pic] 23. [pic]

24. [pic] 25. [pic] 26. [pic]

|Formulas |

| an = a1 + d(n-1) | an = a1 r(n-1) | |

|Sn =[pic] |Sn = a1[pic] |[pic] |

Algebra 2/Trig: Sequence & Series Worksheet #2 Name Date

Find the pattern and tell whether the sequence is arithmetic, geometric, or neither.1. –1, 1, 3, 5, … 2. 1, 8, 27, 64, …

pattern: pattern:

type: type:

3. 2, 4, 8, 16, … 4. –6, -1, 4, 9, …

pattern: pattern:

type: type:

Write the first six terms of the sequence.

5. an = n + 2 6. an = n (n + 1) 7. an = 3n

a1 = a1 = a1 =

a2 = a2 = a2 =

a3 = a3 = a3 =

a4 = a4 = a4 =

a5 = a5 = a5 =

a6 = a6 = a6 =

Write the next term and then write the rule (equation) for the nth term (an).

8. 5, 10, 15, 20, … 9. 3, 7, 11, 15, … 10. 9, 12, 15, 18, …

11. 3, 9, 27, 81, … 12. 5, 4, 3, 2, … 13. [pic]

|Formulas |

| an = a1 + d(n-1) | an = a1 r(n-1) | |

|Sn =[pic] |Sn = a1[pic] |[pic] |

Write the rule for the sequence given the following.

14. r = 0.4, a1 = 5 15. d = 5, a1 = 1 16. 36, 18, 9, …

Determine the pattern, then write the rule (equation) for the following series.

Then find the sum. Write in sigma notation.

17. 2 + 5 + 8 + 11 + 14 + 17 + 20 + 23 + 26 + 29 18. 2 + 8 + 32 + 128 + 512 + 2048 + 8192

Find the sum of the following series. Write in sigma notation.

19. [pic] Sum of the first 14 terms. 20. [pic] Sum of the first 7 terms.

Find the sum of the series.

Hint: For the larger numbers find the pattern and use the Sn formulas.

21. [pic] 22. [pic] 23. [pic]

24. [pic] 25. [pic] 26. [pic]

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