Arithmetic SequencesSequence – a list of numbers or objects (terms)

in a certain orderArithmetic Sequence – the difference b/w one

term and the next is the sameCommon difference – the differences b/w

terms are the same; the common difference is added to each term to get the next

Arithmetic SequencesDetermine if each sequence could be arithmetic. If so, give the common difference.(1) 4, 6, 8, 10, 12, …(2) 14, 12, 11, 9, 8, …(3) 2/9, 1/3, 4/9, 5/9, 2/3, …(4) 99, 92, 85, 78, 71, …(5) 1/2, 1/4, 1/8, 1/16, 1/32, …(6) 9, 6, 3, 0, -3, ...

Arithmetic Sequences

To find a subsequent term, like the 100th for the sequence 5, 7, 9, 11, 13, … w/o finding all 99 terms before, we:(1)Find the common difference (d),(2)Multiply by one less than the term number (ex.: for the 100th term, we would multiply by 99) (n – 1), &(3)Add to the product to the first term (a

1).

For the nth term: an = a

1 + d(n – 1).

Term Name

a1

a2

a3

a4

a5

a6

Term 5 7 9 11 13 15

Pattern 5 + 5(1) 5 + 5(1) 5 + 5(2) 5 + 5(3) 5 + 5(4) 5 + 5(2)

Arithmetic SequencesFind the given term in each arithmetic sequence.(7) 17th term: 5, 7, 9, 11, …(8) 24th term: 2, 6, 10, 14, …(9) 21st term: -4, -8, -12, -16, …(10) 30th term: d = 5, a

1 = 11

Real-Life Application(11) Postage for a first-class letter costs $0.37 for the first ounce, and $0.23 for each additional ounce. If a letter costs $1.52 to mail, how many ounces is it?

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Classwork/HW: ex. 12-36 (evens), 37, 39, 40, 41 on p. 594-595

Arithmetic Sequences Exercises (turn in)Determine if each sequence is arithmetic. If so, give the

common difference.(12) 0.5, 1, 1,5, 2, 2.5, …(14) 0.125, 0.375, 0.875, 1.125, 1.875, …(16) 0.8, 1.2, 1.6, 2, 2.2, …Find the given term for each arithmetic sequence.(18) 11th term: 5, 3, 1, -1, …(20) 50th term: d = 2, a

1 = 1

(22) Mariano received a bonus of $50 for working the day after Thanksgiving, plus his regular wage of $9.45/hr. If his total wages for the day were $135.05, how many hours did he work?

Write the next three terms of each arithmetic sequence.(24) -14, -8, -2, 4, … (26) 0.5, 0.625, 0.75, .0875, …(28) 0.5, 0.4, 0.3, 0.2, …Write the first five terms of each arithmetic sequence.(30) d = 7, a

1 = 3 (32) d = -5, a

1 = 100 (34) d = -4, a

1 = 6

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(36) The 1st term of an arithmetic sequence is 9. The common difference is 11. What position in the sequence is 163?

(37) Julia’s watch loses 5 minutes each day. At noon on Sunday, her watch read 11:55. Write the first four terms of the arithmetic sequence modeling the situation. (Assume a

1 = 11:55.)

(39) A law firm charges an administrative fee of $75, plus a $52.50 fee for each half hour of consultation.(A) What are the first four terms of an arithmetic sequence that represents the rates of the law firm?(B) How long was a consultation if the total bill was $390?

Arithmetic Sequences Exercises (turn in)

Arithmetic Sequences Exercises (turn in)(39) A law firm charges an administrative fee of $75, plus a

$52.50 fee for each half hour of consultation.(A) What are the first four terms of an arithmetic sequence that represents the rates of the law firm?(B) How long was a consultation if the total bill was $390?

(40) Explain how to find the common difference of an arithmetic sequence. What can you say about the terms of a sequence if the common difference is positive? If the common difference is negative?

(41) Write an arithmetic sequence problem for d = 6.5, a7

= -15.