ARITHMETIC SEQUENCES AND SERIES Section 9 2 Precalculus

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ARITHMETIC SEQUENCES AND SERIES Section 9. 2 Precalculus Pre. AP/Dual, Revised © 2016 viet.

ARITHMETIC SEQUENCES AND SERIES Section 9. 2 Precalculus Pre. AP/Dual, Revised © 2016 viet. dang@humble. k 12. tx. us 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 1

DEFINITIONS A. Arithmetic Sequence is a sequence whose consecutive terms have a common difference

DEFINITIONS A. Arithmetic Sequence is a sequence whose consecutive terms have a common difference 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 2

IS IT ARITHMETIC? YES NO 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 3

IS IT ARITHMETIC? YES NO 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 3

STEPS 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 4

STEPS 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 4

EXAMPLE 1 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 5

EXAMPLE 1 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 5

EXAMPLE 1 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 6

EXAMPLE 1 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 6

EXAMPLE 2 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 7

EXAMPLE 2 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 7

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 8

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 8

EXAMPLE 3 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 9

EXAMPLE 3 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 9

EXAMPLE 4 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 10

EXAMPLE 4 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 10

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 11

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 11

EXAMPLE 5 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 12

EXAMPLE 5 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 12

EXAMPLE 6 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 13

EXAMPLE 6 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 13

EXAMPLE 6 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 14

EXAMPLE 6 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 14

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 15

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 15

SIGMA NOTATION upper limit of summation ∑ 5 3 + 6 + 9 +

SIGMA NOTATION upper limit of summation ∑ 5 3 + 6 + 9 + 12 + 15 = ∑ 3 n k=1 index of summation 1/4/2022 2: 33 PM lower limit of summation 9. 2: Arithmetic Sequences 16

STEPS FOR ARITHMETIC SERIES 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 17

STEPS FOR ARITHMETIC SERIES 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 17

EXAMPLE 7 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 18

EXAMPLE 7 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 18

EXAMPLE 8 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 19

EXAMPLE 8 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 19

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 20

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 20

EXAMPLE 9 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 21

EXAMPLE 9 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 21

EXAMPLE 9 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 22

EXAMPLE 9 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 22

EXAMPLE 10 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 23

EXAMPLE 10 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 23

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 24

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 24

EXAMPLE 11 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 25

EXAMPLE 11 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 25

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 26

YOUR TURN 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 26

ASSIGNMENT Page 622 5 -17 EOO, 21 -61 odd 1/4/2022 2: 33 PM 9.

ASSIGNMENT Page 622 5 -17 EOO, 21 -61 odd 1/4/2022 2: 33 PM 9. 2: Arithmetic Sequences 27