1. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Arithmetic Sequences and Partial Sums (Section 8-2)

2. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Sequence: A list of numbers or terms in a pattern. Example: 3, 5, 7, 9,... is a sequence starting at 3 and increasing by 2 each time. Infinite Sequence- a function whose domain is the set of positive integers. The function values a 1, a 2, a 3, …a n are the terms of the sequence. Finite sequence- A sequence in which the domain of the function only consists of the first n terms. Series: The sum of the terms of a sequence.

3. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Arithmetic Sequence- A sequence whose differences between consecutive terms in a sequence are the same The sequence a 1, a 2, a 3, a 4, …, a n is arithmetic if a 2 – a 1 = a 3 – a 2 = a 4 – a 3 =…=a n – a n-1 d is called the common difference

4. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Determine if the sequence is arithmetic, if it is find the common difference. Example 1 7, 11, 15, 19, …

5. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Determine if the sequence is arithmetic, if it is find the common difference. Example 2 2, -3, -8, -13, …

6. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Determine if the sequence is arithmetic, if it is find the common difference. Example 3 1, 4, 9, 16, …

7. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Determine if the sequence is arithmetic, if it is find the common difference. Example 4

8. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. n th term of an arithmetic sequence: a n = a 1 + (n-1)d

9. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Write the first five terms of the sequence. Determine whether or not the sequence is arithmetic. If it is find the common difference. (Assume n begins with 1.) Example 5

10. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find a formula for a n for the arithmetic sequence, Example 6

11. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find a formula for a n for the arithmetic sequence, Example 7

12. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find a formula for a n for the arithmetic sequence, Example 8

13. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. The first two terms of the arithmetic sequence are given. Find the missing term. Example 9

14. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Recursive sequence- a sequence where you are given the first one or two terms and the other terms are defined using previous terms.

15. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Write the first five terms of the sequence defined recursively. Example 10

16. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Write the first five terms of the sequence defined recursively. Example 11

17. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Write the first five terms of the sequence defined recursively. Example 12

18. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. HW #46 pg 587-591 (57, 59, 61, 63, 65) HW #47 pg 598-599 (1, 3, 5, 9, 13, 17-23 odd, 27, 29, 35)

19. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Factorial- (if n is a positive integer) n! = 12 3 4 …(n-1) n. Special case: 0! = 1

20. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find each value. Example 13 4!Example 14 5!

21. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Write the first five terms of sequence. (Assume n begins with 0). Example 15

22. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Simplify the factorial expression. Example 16

23. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Simplify the factorial expression. Example 17

24. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Simplify the factorial expression. Example 18

25. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Summation Notation: The sum of the first terms n of a sequence is represented by, where i is the index of summation, n is the upper limit of summation, 1 is the lower limit of summation. Properties of Sums 1) 2) 3)4)

26. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence.

27. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find the sum. Example 19

28. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find the sum. Example 20

29. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Sum of an Arithmetic Sequence:

30. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find the sum of the finite arithmetic sequence. Example 21 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

31. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Find the indicated n th partial sum of the arithmetic sequence. Example 22

32. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Example 23 Sum of the integers from 1 to 100.

33. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Example 24 Find the 150 th partial sum of the arithmetic sequence 5, 16, 27, 38, 49, ….

34. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. Example 25 An auditorium has 20 rows of seats. There are 20 seats in the first row, 21 seats in the second row, 22 seats in the third row, and so on. How many seats are there in all 20 rows?

35. Essential Question: How do you find the nth term and the sum of an arithmetic sequence? Students will write a summary describing the steps to find the nth term and sum of an arithmetic sequence. HW #38 pg 598—599 (1, 3, 13, 17-23 odd, 27, 35, 39, 41, 53, 55, 57, 61, 63)