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NAME:_________________________ PERIOD:_____
MATH 2: Sequences and Series Agenda
(5% of your grade)
DayTopic/EQClasswork/HomeworkStampSept. 26
MonWhat is an arithmetic sequence?
WS #1Sept. 27
TuesWhat is an arithmetic series, and how do I find the sum of an arithmetic series? WS #2
Sept. 28
WedHow do I find the sum of an arithmetic series when Im not given my n term?WS #3
WS #4Sept. 29
ThursHow do I write arithmetic series in summation notation?WS #5
Study for Quiz Sept. 30
FriWhat have I learned about arithmetic sequences?Quiz: Arithmetic Sequences and Series (Not WS#3)
Oct. 3
MonHow do I evaluate a series in summation notation? WS #6Oct. 4
Tues.How confident am I arithmetic sequences and series?CFA
Oct. 5
Wed.How confident am I arithmetic sequences and series?Review Sheet (WS#7)Oct. 6
Thurs.What I have learned this unit?TESTStandards:
Explore arithmetic series and various ways of computing their sums.
Explore sequences of partial sums of arithmetic series as examples of
quadratic functions.
Arithmetic Sequences Worksheet #1 Name: _______________________ Hr:____
Write the equation for the arithmetic series below.
1. EMBED Equation.DSMT4
2. 10, 100, 190, 280
3. EMBED Equation.DSMT4 4. 4, 1, -2, -5
e. EMBED Equation.DSMT4
5. EMBED Equation.DSMT4 6. 10, 8, 6, 4, .7. EMBED Equation.DSMT4 8. EMBED Equation.DSMT4 9. EMBED Equation.DSMT4
10. EMBED Equation.DSMT4 11. EMBED Equation.DSMT4 12. EMBED Equation.DSMT4
13. EMBED Equation.DSMT4 14. EMBED Equation.DSMT4 15. EMBED Equation.DSMT4
16. Find EMBED Equation.DSMT4 in # 1 17. Find EMBED Equation.DSMT4 in # 2 18. Find EMBED Equation.DSMT4 in #11.
19. Given EMBED Equation.DSMT4 . Find: d= _______. EMBED Equation.DSMT4 EMBED Equation.DSMT4
20. Write the first 5 terms of the sequence EMBED Equation.DSMT4
Investigating Sums of Arithmetic Sequences
STEP 1: Add the given terms of the sequence to find the sum for those terms.
STEP 2: Calculate the average of the first and last terms of the sequence.
STEP 3: Multiply the average found in step 2 by the number of terms in the sequence.
STEP 4: Record your answers in a table.
SequencesSumAverage of
1st and last termMultiply Avg. by number of terms2, 5, 8, 11, 141, 8, 15, 22-1, 1, 32, 11, 20, 29, 38, 47, 56-25, -29, -33, -37, -4120, 16, 12, 8, 4, 0
Draw Conclusions:
1. Compare your answers from Steps 1 and 3. What do you notice?
Write a sentence that explains how to calculate the sum of the first n terms of a sequence
without adding all of the terms.
Write a formula for the explanations you gave in Exercise 3. Use a1 to represent the first term,
an to represent the last term, and n to represent the number of terms.
5. Use your formula to find the sum of the terms in each of the following sequence:
a. 3, 9, 15, 21 b. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
Arithmetic Series: Worksheet #2 Name:__________________________ Period:______
Use the series formula and show your work.
Given the series 5, 8, 11, 14.
1. Find the sum of the first 4 terms. 2. Find EMBED Equation.DSMT4 .
Given the series 8, 7, 6, 5, 4, 3, 2.
3. Find the sum of the first 7 terms. 4. Find EMBED Equation.DSMT4 .
Given EMBED Equation.DSMT4
5. Find the sum of the first 12 terms. 6. Find the sum of the first 20 terms.
Given EMBED Equation.DSMT4
7. Find the sum of the first 9 terms. 8. Find the sum of the first 11 terms.
Given EMBED Equation.DSMT4
9. Find the sum of the first 99 terms. 10. Find the sum of the first 200 terms.
Arithmetic Sequences: Worksheet #3 Name:______________________ Period:__________
1. Find the sum of the first 200 terms of the sequence 5, 7, 9, 11..
2. Find the sum of the first 150 terms of the sequence 20, 15, 10, 5..
3. Find the sum of the first 50 terms of the sequence 2, 4, 6, 8..
4. Find EMBED Equation.DSMT4 of the sequence 12, 11, 10, 9..
5. Find the sum of the first 100 odd numbers.
6. Find the sum of the first 200 even numbers.
7. Find the sum of the first 600 multiples of 5.
8. Find the sum of the first 50 multiples of 3.
Review for Quiz: Worksheet #4 Name:__________________ Period:___
Write the rule for the sequence below. Give the requested information about the sequence.
Given Sequence InformationRuleAdditional Request1. 6, 7, 8, 9. EMBED Equation.DSMT4 EMBED Equation.DSMT4 2. 12, 10, 8, 6. EMBED Equation.DSMT4 EMBED Equation.DSMT4 3. 2, 12, 22, 32 EMBED Equation.DSMT4 EMBED Equation.DSMT4 4. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 5. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 6. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 7. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4 8. EMBED Equation.DSMT4 EMBED Equation.DSMT4 EMBED Equation.DSMT4
Find the sum of the following. Make sure you use the formula.
9. The first 12 terms of the sequence EMBED Equation.DSMT4 10. The first 21 terms of the sequence EMBED Equation.DSMT4
11. EMBED Equation.DSMT4 if the sequence is 3, 6, 9, 12, 15, 18 12. 100, 98, 96, 94, 92, 90, 88, 86, 84, 82, 80, 78
13. The first 7 terms of the sequence 20, 30, 40, 50, 60, 70, 80.14. EMBED Equation.DSMT4 if the sequence is 1, 5, 9, .
1. EMBED Equation.DSMT4 2. EMBED Equation.DSMT4 3. EMBED Equation.DSMT4 4. EMBED Equation.DSMT4
5. EMBED Equation.DSMT4 6. EMBED Equation.DSMT4 7. EMBED Equation.DSMT4 8. EMBED Equation.DSMT4
9. -36 10. 672 11. 108 12. 1068 13. 350 14. 190
Summation Notation: Worksheet #5 Name:_______________________Period:______
Write the following in summation notation.
1. 4, 8, 12, 16, 20 2. 20, 14, 8, 2, -4, -10
3. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 4. 5, 10, 15
5. 4, 8, 12, .. 100 6. 32, 30, 28, . 14
Write out the series represented below.
7. EMBED Equation.DSMT4 8. EMBED Equation.DSMT4 9. EMBED Equation.DSMT4
10. EMBED Equation.DSMT4 11. EMBED Equation.DSMT4 12. EMBED Equation.DSMT4
Summation Notation: Worksheet #6 Name:________________________ Period:______
Find the sum represented below.
1. EMBED Equation.DSMT4
2. EMBED Equation.DSMT4 3. EMBED Equation.DSMT4 4. EMBED Equation.DSMT4 5. EMBED Equation.DSMT4 6. EMBED Equation.DSMT4
7. EMBED Equation.DSMT4 8. EMBED Equation.DSMT4 9. EMBED Equation.DSMT4
10. EMBED Equation.DSMT4 11. EMBED Equation.DSMT4 12. EMBED Equation.DSMT4
Review of Arithmetic Sequences and Series: WS #7 Name:___________________ Period:_______
1. Write a rule for the arithmetic sequences below.
a. 7, 12, 17, 22
b. 10, 9, 8, 7.
c. EMBED Equation.DSMT4
d. EMBED Equation.DSMT4
e. EMBED Equation.DSMT4 f. EMBED Equation.DSMT4
g. EMBED Equation.DSMT4 h. EMBED Equation.DSMT4
2. Write the first five terms of the sequence EMBED Equation.DSMT4 . Find EMBED Equation.DSMT4 .
(Continued on the next page) (WS #7 CONTINUED)
a. EMBED Equation.DSMT4 b. EMBED Equation.DSMT4
c. EMBED Equation.DSMT4 d. The first 50 even numbers.
e. 5, 8, 11, 14. 44
f. The first 49 terms of the sequence EMBED Equation.DSMT4
g. The first 30 terms of the sequence
-7, -3, 1, 5.
3h. The first 100 odd numbers.
3. Find the sum of the sequence below:
ANSWERS: (
1a. EMBED Equation.DSMT4 1b. EMBED Equation.DSMT4 1c. EMBED Equation.DSMT4 1d. EMBED Equation.DSMT4 1e. EMBED Equation.DSMT4
1f. EMBED Equation.DSMT4 1g. EMBED Equation.DSMT4 1h. EMBED Equation.DSMT4 2. 3, 7, 11, 15, 19. 399
3a. 330 3b. -288 3c. 1050 3d. 2550 3e. 343 3f. 4459 3g. 1530 3h. 10,000
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a 2
= = 1 2 d = ="- 2 O b j I n f o a q E q u a t i o n N a t i v e r 1 _ 1 3 3 4 3 9 1 5 3 0 d F Y"Y O l e
w C o m p O b j c e x i O b j I n f o f z E q u a t i o n N a t i v e { + _ 1 3 3 4 3 9 1 6 2 1 b l i F #YXY
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a 8
= = 4 0 d = = 4 O l e
C o m p O b j h j i O b j I n f o k E q u a t i o n N a t i v e =
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a 3
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= = 1 3
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a 8
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= = 4 4
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Times New Roman Symbol Courier New MT Extra !/ED/APG_AP APA E%B_A C_A E*_HA @AHA*_D_E_E_A
a 3
= = 9 a 5
= = 1 0
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a n
= = 4 n "- 1
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a 1 0 0
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p 2 i + + 6 i = = 1 1 5
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p "- 2 i + + 3 i = = 1 1 8
" O b j I n f o E q u a t i o n N a t i v e , _ 1 3 4 6 1 3 1 5 0 4 F YY O l e
C o m p O b j i O b j I n f o E q u a t i o n N a t i v e _ 1 3 3 4 4 7 5 2 8 7 F YY
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p 5 n n = = 1 2 0
" O l e
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a n
= = 4 n "- 9
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a n
= = 5 n + + 2
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a n
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a n
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a n
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a n
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