Finding the sum of the first n even integers
(remember, n represents the # of even integers
and Finding the sum of the first n consecutive integers

1. find the sum of the first 75 even integers.
2. find the sum of the first 100 even integers.
3. how many even integers are there between 1 and 60?
4. how many even integers are there between 1 and 200?
5. how many even integers are there between 1 and 500?
6. 2+4+6+...+60=?
7. 2+4+6+...+200=?
8. 2+4+6+...+500=?
9. if 2+4+6+...+1000=? is the same as finding the sum of the first 500 even integers, then 2+4+6+...+ is the same as ....?
10. if 2+4+6+...+450=? is the same as finding the sum of the first 225 even integers, then 2+4+6+...+ is the same as ....?
11. if 2+4+6+...+840=? is the same as finding the sum of the first 420 even integers, then 2+4+6+...+ is the same as ....?
12. 58+60+62+...600=?
13. 34+36+38+...+168=?
14. 88+90+92+...+792=?
15. find the sum of the first 150 consecutive integers.
16. find the sum of the first 75 consecutive integers.
17. find the sum of the first 221 consecutive integers.
18. 1+2+3+...+ 123=?
19. 1+2+3+...+242=?
20. 1+2+3+...+650=?
21. 66+67+68+...+431=?
22. 90+91+92+...+357=?
23. 44+45+46+...+242=?

For numbers 24-28, first determine which nth term you need to use (n squared, n(n+1), or n(n+1)/2). Be sure you can justify your answer. Then, solve the problem.

24. 56+58+60+...+548=?

25. 1+3+5+...+453=?

26. 45+46+47+...+226=?

27. 2+4+6+...+888=?

28. 39+41+43+...199=?

29. Find the nth term of the following sequence: 1, 2, 15, 40, 77, 126

30. Find the value of the 50th term: 0, 0, 2, 6, 12, 20 (this problem gives me warm fuzzzies...lol)

Finding sum of a series of odd numbers

For numbers 1-5, find the nth term.

1. 28, 45, 66, 91, 120
2. 7, 24, 45, 70, 99
3. 15, 21, 28, 36, 45
4. 5, 28/3, 15, 22, 91/3
5. -2, 7/2, 15, 65/2, 56
6. Find the sum of the first 40 odd numbers.
7. Find the sum of the first 121 odd numbers.
8. Find the sum of the first 343 odd numbers.
9. 1+3+5+7+...+79=?
10. 1+3+5+7+...+241=?
11. 1+3+5+7+...+685=?
12. Given that the sum of the first 50 odd numbers is the same as the mathematical problem 1+3+5+7+9+11+...+99, rewrite the following sentence as a mathematical problem: the sum of the first 150 odd numbers is the same as ......
13. Given that the sum of the first 50 odd numbers is the same as the mathematical problem 1+3+5+7+9+11+...+99, rewrite the following sentence as a mathematical problem: the sum of the first 242 odd numbers is the same as ......
14. Given that the sum of the first 50 odd numbers is the same as the mathematical problem 1+3+5+7+9+11+...+99, rewrite the following sentence as a mathematical problem: the sum of the first 400 odd numbers is the same as ......
15. 55+57+59+...+311=?
16. 213+215+217+...+501=?
17. 457+459+461+...+975=?
18. 99+101+103+...+445=?
19. 25+27+29+...+1013=?
20. 77+79+81...+367=?

More nth Term Problems

For numbers 1-10, find the nth term. Then find the value of the 20th term.

1. 8, 13, 18, 23
2. 2, 5, 8, 11
3. 9, 13, 17, 21
4. 6, 14, 22, 30
5. 17, 27, 37, 47
6. -3, 10, 35, 72
7. 12, 40, 66, 112
8. 28, 63, 110, 169
9. -5/2, 0, 13/2, 17, 63/2
10. -5/2, 3, 21/2, 20
11. Find the sum of the first 100 odd numbers.
12. Find the sum of the first 25 odd numbers.
13. Find the sum of the first 50 odd numbers.
14. How many odd numbers are there between 1 and 299?
15. How many odd numbers are there between 1 and 75?
16. How many odd numbers are there between 1 and 183?
17. 1+3+5+...+299=?
18. 1+3+5+...+75=?
19. 1+3+5+...183=?
20. 1+3+5+...+247=?

#1.5

• (3, 4)
• (9-14)
• (20, 21, 24, 25)

#1.4
Find the nth term for each sequence. After you find the nth term, I want you to tell me what the value of the 20th term will be (that means substitute n with 20 after you get your answer. For example, if you get 2n+5 as your nth term, then the value of the 20th term would be equal to 2(20) +5 or 45)

1. 3, 9, 15, 21, 27, 33
2. 11, 23, 35, 47, 59, 71
3. -4, 4, 12, 20, 28, 36
4. 0, 7, 14, 21, 28, 35
5. do in class tomorrow
6. do in class tomorrow
7. do in class tomorrow
8. do in class tomorrow
9. do in class tomorrow

#1.5

Find the nth term for each sequence. After you find the nth term, I want you to tell me what the value of the 20th term will be (that means substitute n with 20 after you get your answer. For example, if you get (4n+1)(n+3) as your nth term, then the value of the 20th term would be equal to [4(20)+1](20+3) = (81)(23)= 1863 ).

1. 4, 8, 12, 16, 20, 24
2. 5, 7, 9, 11, 13, 15
3. do in class tomorrow
4. do in class tomorrow
5. 2, 9, 20, 35, 54, 77
6. 0, 3, 8, 15, 24, 35
7. 4, 10, 18, 28, 40, 54
8. 6, 21, 40, 63, 90, 121

Some of these may be challenging for some of you and for some of you, this is easy. If you're struggling, call a friend or go online into the chat room. If this is easy for you, go into the chat room and help somebody. First of all, it'll make you feel good. Second of all, you'll reinforce your understanding by explaining it to somebody else. Third of all, what goes around comes around...one of these days when you're the one struggling, someone will be more than likely to remember your generosity and want to help you out.

#1.2 Inductive Reasoning

• Using inductive reasoning, find the next two terms of the sequence. Be sure to SHOW your work!

• 2. 180, 360, 540, 720, ?, ?
• 4. 1, 3, 6, 10, 15, 21
• 6. W, T, Q, N, K, H
• 8. a, 6, c, 12, e, 18
• 10. A, B, D, G, K
• 12. 1, 3, 4, 7, 11, 18
• 14. 1, 3, 7, 15, 31, 63
• 16. 3, 5, 11, 29, 83, 245
• 18. 3, -12, 48, -192, 768
• 20. 1/2, 1/3, 1/8, 1/16

be sure to get your supplies by Friday!!!!! Signed Rules must be turned in to me by Friday, August 28, 2010!!!!