1.1 Cont.

Warm-up (IN)

1. Give the first 4 terms of the sequence:a. b.

2. Write a rule for the nth term of the sequence: 6, 1, -4, -9, …

Learning Objective: to continue to find terms of sequences and then to find the sum of an arithmetic series

-2, 8, 18, 28

5, -2, -9, -161 5, 7a d

1 2, 10a d

11 5na n

Notes!

Ex 1 – if find 1 2, 7a d 5a 1 ( 1)na a n d

5a 2 (5 1) 7

5a 2 (4) 7

5a 2 28

5a 30

Ex 2 – find for 5, 11, 17, 23, …10a

10a 5 (10 1) 6

10a 5 (9) 6

10a 59

Ex 3 – find if and 15a 3 30a 10 9a First we need to find d

Pretend…

1 30a then… 8 9a

9 30 (8 1) d

1 ( 1)na a n d

9 30 7d21 7d

3 d

also… 15 13a a

13a 30 (13 1) 3

13a 30 (12) 3

13a 30 36

13a 6or…

15a 6

Ex 4 – find the missing numbers in the arithmetic sequence

2, ____, ____, ____, 18First we need to find d

1 ( 1)na a n d

18 2 (5 1) d

18 2 4d

16 4d

4 d

6, 10, 14,

Arithmetic Series – The expression formed by adding the terms of an arithmetic sequence

5+9+13+17+21+25 We can only find the sum if the series is finite

303030

30x3 =90

Sum formula – 1

2n

n

a a nS

Ex 5 – find 7+5+3+1+-1+-3+-5

nS

2

7 5 77

Ex 6 – find 12+15+18+21+…+42First we need to find n

1 ( 1)na a n d

42 12 ( 1)n 3

30 3 3n 33 3n

11 n

nS

2

12 42 11297

W2L – the difference between a sequence and a series is…

Ex 7 – find ifnS 1 4, 3, 5a d n

First we need to find

the last term

1 ( 1)na a n d

na 4 (5 1) 3na 8

nS

2

4 8 510

HW – finish worksheet

Out – find 8+5+2+-1+-4+-7+-10+-13

Summary – Today I learned how to…

Don’t forget about POW!!